What is cost matrix analysis. Analysis, matrix. The introduction of matrix tools in the analysis and planning of the enterprise

In strategic planning and marketing, quite a lot of matrices of one direction or another are used. There is a need to systematize these matrices, as well as to gradually introduce the matrix approach at all stages of strategic analysis and planning.

Levels of strategic planning in the matrix dimension. In strategic planning, one can single out the corporate level, the business level, and the functional level.

Strategic planning matrices at the corporate level analyze the businesses included in the corporation, i.e. help to carry out portfolio analysis, as well as analysis of the situation in the corporation as a whole.

The business layer includes matrices that are relevant to a given business unit. Matrices and refer most often to one product, analyze the properties of this product, the situation on the market for this product, etc.

Functional level matrices explore the factors that affect the functional areas of the enterprise, of which the most important are marketing, personnel.

Classification of matrices of strategic analysis and planning.

Existing strategic analysis and planning matrices explore various aspects this process. The classification of matrices is necessary to identify patterns and features of the application of the matrix method in strategic analysis and planning.

Matrices according to existing features can be classified as follows:

  • Classification by the number of cells under study.
  • The more cells the matrix contains, the more complex and informative it is. In this case, it is possible to divide the matrices into four groups. The first group includes matrices consisting of four cells. In the second group there are matrices consisting of nine cells, in the third - from sixteen, in the fourth - more than sixteen cells.

  • Classification by object of study.
  • Classification according to the object of study divides the matrices into groups depending on the object under study. In the Awareness-Attitude matrix, the object of study is the staff, as well as in the matrix “The impact of pay on group relationships”. Another object of study is the portfolio of the company. Shell/DPM, BCG matrices can serve as examples in this group.

  • Classification according to the information received.
  • This classification divides the matrices into two groups according to the information received: either quantitative or semantic. In this group, an example of a matrix formed due to information in the form of a number is the matrix of the vector of the economic state of the organization, and formed due to logical information - a matrix of the main forms of associations.

The introduction of matrix tools in the analysis and planning of the enterprise.

At the first stage, it is proposed to make a primary analysis of the enterprise. Three matrices have been selected for this purpose. The SWOT matrix is ​​widely described in the literature. The MCC matrix involves an analysis of the compliance with the mission of the enterprise and its main capabilities. vector matrix economic development enterprise is a table that presents the numerical data of the main indicators of the enterprise. From this matrix, you can draw information for other matrices, as well as draw various conclusions based on these data already at this stage.

The second stage of application matrix methods is market and industry analysis. It analyzes the markets in which the company operates, as well as the industry as a whole. The main ones in the “Market” subgroup are the BCG matrix, which examines the dependence of growth rates and market share, and the GE matrix, which analyzes the comparative attractiveness of the market and competitiveness in the industry and has two varieties: the Daya variant and the Monienson variant. The "Industry" subgroup contains matrices that study the industry environment, patterns of industry development. The main one in this subgroup is the Shell/DPM matrix, which examines the relationship between industry attractiveness and competitiveness.

The next steps in strategic planning are differentiation analysis and quality analysis. Differentiation and quality act in this case as components with the help of which it is possible to obtain the desired result. There are three matrices in the "Differentiation" group. The matrix "Improving the competitive position" allows you to visually identify patterns and dependencies of differentiation on market coverage. The "Differentiation - Relative Cost Effectiveness" matrix reveals the relationship between relative cost effectiveness in a given market and differentiation. The Performance-Innovation/Differentiation matrix shows the relationship between the performance of a given business unit and the adoption of innovations.

The object of study of the "Quality Analysis" group is the identification of factors and patterns that affect such an aspect as the quality of products. A group can include two matrices. The Pricing Strategies matrix positions products based on quality and price. The matrix "Quality - resource intensity" determines the ratio of the quality of the product produced and the resources spent on it.

The "Management Analysis" and "Marketing Strategy Analysis" groups are not included in the step-by-step implementation of the matrix method in strategic planning. These groups are isolated. The matrices that make up these groups can be applied at all stages of strategic planning and address issues of functional planning. The Control Analysis group consists of two subgroups. The first subgroup - "Management" - considers the management of the company as a whole, the processes that affect the management, management of the company. The subgroup "Personnel" considers the processes taking place between colleagues, the influence of various factors on the performance of staff.

In the proposed scheme of strategic analysis and planning in each group, the matrices interact with each other, but one cannot rely on the result or conclusion of only one matrix - it is necessary to take into account the conclusions obtained from each matrix in the group. After the analysis in the first group, the analysis in the next one is carried out. Analysis in the "Management" and "Marketing Strategy" groups is carried out at all stages of the analysis in strategic planning.

Characterization of individual matrices

SWOT analysis is one of the most common types of analysis in strategic management today. SWOT: Strengths (Forces); Weaknesses (Weaknesses); Opportunities (Opportunities); Threats. SWOT analysis allows you to identify, structure the strengths and weaknesses of the company, as well as potential opportunities and threats. This is achieved by comparing the internal strengths and weaknesses of their company with the opportunities that the market gives them. Based on the quality of compliance, a conclusion is made about the direction in which the business should develop, and ultimately the distribution of resources by segments is determined.

The purpose of the SWOT analysis is to formulate the main directions for the development of the enterprise through the systematization of the available information about the strengths and weaknesses of the company, as well as potential opportunities and threats.

The most attractive thing about this method is that the information field is formed directly by the leaders themselves, as well as by the most competent employees of the company, based on the generalization and coordination of their own experience and vision of the situation. A general view of the matrix of the primary SWOT analysis is shown in Fig.1.

Fig.1. Matrix of primary strategic SWOT - analysis.

Based on a consistent consideration of factors, decisions are made to adjust the goals and strategies of the enterprise (corporate, product, resource, functional, managerial), which, in turn, determine the key points of organizing activities.

Analysis of a company's business portfolio should help managers evaluate the company's field of activity. The company should strive to invest in more profitable areas of its activities and reduce unprofitable ones. The first step of the management in the analysis of the business portfolio is to identify the key areas of activity that define the mission of the company. They can be called strategic elements of business - SEB.

In the next step of the business portfolio analysis, management must assess the attractiveness of the various SEBs and decide how much support each of them deserves. In some companies, this happens informally during the course of work. Management examines the totality of the activities and products of the company and, guided by common sense, decides how much each SEB should bring and receive. Other companies use formal methods for portfolio planning.

Formal methods can be called more precise and thorough. Among the most well-known and successful methods of business portfolio analysis using formal methods are the following:

  • Boston Consulting Group (BCG) method;
  • General Electric (GE) method.

The BCG method is based on the principle of analysis of the growth/market share matrix. This is a portfolio planning method that evaluates a company's SEB in terms of their market growth rate and the relative market share of those items. SEBs are divided into "stars", "cash cows", "dark horses" and "dogs" (see Fig. 2).

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Fig.2. BCG Matrix.

The vertical axis in Figure 2, the market growth rate, determines the measure of market attractiveness. The horizontal axis, relative market share, determines the strength of a company's position in the market. When dividing the growth/market share matrix into sectors, four types of SEBs can be distinguished.

"Stars". Rapidly developing lines of business, products with a large market share. They usually require heavy investment to sustain their growth. Over time, their growth slows down, and they turn into "cash cows".

"Cash Cows". Lines of business or products with low growth rates and a large market share. These sustainable, successful SEBs require less investment to maintain their market share. At the same time, they bring in high income, which the company uses to pay its bills and to support other SEBs that require investment.

"Dark Horses" Business elements with a small share of high-growth markets. They require a lot of funds even to maintain their market share, let alone increase it. Management should carefully consider which "dark horses" should be turned into "stars" and which should be phased out.

"Dogs". Lines of business and products with low growth rate and small market share. They may generate enough income to support themselves, but do not promise to become more serious sources of income.

Each SEB is submitted for given matrix in proportion to its share in the company's gross income. After classifying the SES, the company must determine the role of each element in the future. For each SEB, one of four strategies can be applied. A company may increase investment in an element of the business in order to gain market share for it. Or it can invest just enough to keep the SEB share at the current level. It can drain resources from the SEB by withdrawing its short-term monetary resources over a certain period of time, regardless of long-term consequences. Finally, it can deinvest in the SEB by selling it or going into a phase-out and use the resources elsewhere.

Over time, the SEB changes its position in the growth/market share matrix. Each SEB has its own life cycle. Many SEBs start as "dark horses" and, under favorable circumstances, move into the category of "stars". Later, as the market growth slows, they become "cash cows" and, finally, at the end of their life cycle, they fade away or turn into "dogs". Companies need to continuously introduce new products and activities so that some of them become "stars" and then "cash cows" that help finance other SEBs.

Matrix methods play a very important role in strategic analysis, planning and marketing. The matrix method is very convenient - this explains its prevalence. However, the use of only matrix methods is not sufficient, since matrices allow you to explore strategic planning and marketing from separate angles, and do not show the full picture, but in combination with other methods, the matrix approach makes it possible to visually see the patterns in the processes taking place in the enterprise and make correct conclusions.

Table 1. Matrix tools in the analysis and planning of the organization's activities

Levels of problem solving Matrix Main characteristics
1 Primary Analysis SWOT matrix Analysis of the strengths and weaknesses of the enterprise, opportunities and threats
2 Matrix MCC Analysis of compliance with the mission of the enterprise and its main capabilities
3 Matrix of the vector of economic development of the enterprise Analysis of statistical data
4 Market/industry analysis BCG Matrix Analysis of growth rates and market share
5 Matrix GE Analysis of comparative market attractiveness and competitiveness
6 ADL Matrix Industry life cycle analysis and relative market position
7 Matrix HoferSchendel Analysis of the position among competitors in the industry and the stage of market development
8 Ansoff matrix
(“market-product”)
Analysis of strategy in relation to markets and products
9 Porter matrix
(five competitive forces)
Analysis of strategic prospects for business development
10 Elasticity matrix of competitive response in the market Analysis of the company's action on the factors of competitiveness of the product, depending on the elasticity of the reaction of the priority competitor for the product
11 Product grouping matrix Product grouping analysis
12 Matrix “Impact Uncertainty” Analysis of the level of impact and degree of uncertainty when entering a new market
13 Industry Cooper matrix Analysis of industry attractiveness and business strength
14 ShellDPM Matrix Analysis of the attractiveness of a resource-intensive industry depending on competitiveness
15 Downturn Strategies Matrix Analysis of competitive advantages in the industry environment
16 Matrix of basic join forms Analysis of association in an industry environment
17 Analysis of differentiation Competitive Position Improvement Matrix Analysis of differentiation and market coverage
18 Matrix “Differentiation Relative Cost Effectiveness” Analysis of differentiation and relative cost effectiveness
19 Matrix “Performance - Innovation/Differentiation” Analysis of innovation/differentiation and performance
20 Quality analysis Matrix “Price-quality” Product positioning depending on quality and price
21 Matrix
“Quality-resource intensity”
Analysis of the dependence of quality on resource intensity
22 Marketing strategy analysis Brand Family Extension Strategy Matrix Analysis of the dependence of distinctive advantages and segmentation of the target market
23 Matrix “Awareness - attitude to the brand of goods” Analysis of the relationship between gross profit margin and sales response
24 Marketing Channel Matrix Analysis of the relationship between the pace of market development and the value added by the channel
25 Matrix “Contact- service adaptation level” Analysis of the dependence of the level of adaptation of services to the requirements of clients on the degree of contact with the client
26 Matrix
“Marketing Diagnostics”
Analysis of the dependence of the strategy on the implementation of the strategy
27 Management Analysis
Management
Matrix of strategic management methods Analysis of the dependence of strategy and the impact of planning
28 Matrix of the strategic management model Analysis of the dependence of the management model on the type of changes
29 Hersey-Blanchard matrix Analysis of the situational leadership model
30 Ohio University Leadership Style Dimension Combinations Matrix Analysis of Combinations of Leadership Style Dimensions
31 Matrix “Management Grid” Leadership type analysis
32 Staff Matrix "Change - in the organization" Analysis of the dependence of changes occurring in the organization and resistance to these changes
33 Matrix of the influence of payment on relationships in the group Analysis of the dependence of relationships in the group on the differentiation of payment
34 Matrix of types of inclusion of a person in a group Analysis of the relationship between the attitude to the values ​​of the organization and the attitude to the norms of behavior in the organization
35 Matrix “Key Business Capabilities” Analysis of the market and key business capabilities
36 Matrix “Importance of work” Analysis of the dependence of the performance of work on the importance
37 Matrix of existing formal systems of performance criteria Analysis of existing formal systems of performance criteria
38 Performance management results matrix Analysis of the results of management of performance criteria
39 Blake-Mouton matrix Analysis of the dependence of the performance of work on the number of people and on the number of tasks
40 McDonald Matrix Performance analysis

Historically, the first model of corporate strategic planning is considered to be the so-called “growth-share” model, which is better known as the Boston Consulting Group (BCG) model.

This model is a kind of mapping of the positions of a particular type of business in a strategic space, defined by two axes (x, y), one of which is used to measure the growth rate of the market for the corresponding product, and the other - to measure the relative share of the organization's products in the market of the product in question.

The emergence of the BCG model was the logical conclusion of one research work, conducted at one time by a specialist of the consulting company Boston Consulting Group.

In the process of studying various organizations that produce 24 main types of products in 7 industries (electricity, plastics, non-ferrous metals, electrical equipment, gasoline, etc.), empirical facts were established that when production volumes are doubled, variable costs of production units of production are reduced by 10-30%.

It has also been found that this trend occurs in almost every market sector.

These facts became the basis for the conclusion that variable production costs are one of the main, if not the main, factor in business success and determines the competitive advantages of one organization over another.

Statistical methods were used to derive empirical dependencies describing the relationship between production costs, units of production and production volume. And one of the main factors of competitive advantage was put in one-to-one correspondence with the volume of production, and therefore, with what market share of the corresponding products this volume occupies.

The main focus of the BCG model is on the cash flow of the enterprise, which is directed either to the conduct of operations in a particular business area, or arises from such operations. It is believed that the level of income or cash flow is in a very strong functional dependence on the growth rate of the market and the relative share of the organization in this market.

The growth rate of an organization's business determines the rate at which the organization will use cash.

It is generally accepted that at the stage of maturity and at the final stage of the life cycle of any business, a successful business generates cash, while at the stage of development and growth of a business there is an absorption of cash.

Conclusion: To maintain the continuity of a successful business, the money supply resulting from the implementation of a "mature" business must be partly invested in new areas of business that promise to become generators of future income for the organization.

In the BCG model, the main commercial goals of the organization are the growth of the mass and the rate of profit. At the same time, the set of acceptable strategic decisions regarding how these goals can be achieved is limited to 4 options:

  • 1) increase the share of the organization's business in the market;
  • 2) the struggle to maintain the share of the organization's business in the market;
  • 3) maximum use of the position of the business in the market;
  • 4) exemption from this type of business.

The decisions that the BCG model suggests depend on the position of the particular type of business of the organization, the strategic space formed by the two coordinate axes. The use of this parameter in the BCG model is possible for 3 reasons:

a growing market, as a rule, promises a return on investment in the near future this species business.

increased market growth rates affect the amount of cash with a “-” sign even in the case of a fairly high rate of return, as it requires increased investment in business development.

There are two BCG models: classic and adapted. Consider the Classical Model:

Structure of the Classic Model:

The abscissa shows the measurement of some competitive positions of the organization in this business as the ratio of the organization's sales in this business to the sales of the largest competitor in this business area.

In the original version of BCG, the abscissa scale is logarithmic. Thus, the BCG model is a 2 * 2 matrix, on which business areas are displayed as circles centered at the intersection of coordinates formed by the corresponding market growth rates and the relative share of the organization in the corresponding market.

Each plotted circle characterizes only 1 business - an area characteristic of this organization.

The size of the circle is proportional to the total size of the entire market. Most often, this size is determined simple addition the organization's business and the corresponding business of its competitors.

Sometimes a segment is allocated on each circle, characterizing the relative share of the organization's business area in a given market, although this is not necessary to obtain strategic conclusions in this model.

The division of the axes into 2 parts is not done by chance. At the top of the matrix are business areas with above-average growth rates. At the bottom, respectively, lower.

In the original BCG model, it is assumed that the border between high and low growth rates is a 10% increase in sales per year.

Each of these squares is given figurative names (for example: the BCG matrix is ​​called "Zoo").

"Stars": these are new business areas that occupy a relatively large share of a booming market that brings high profits. These business areas can be called leaders in their industries, as they bring the organization a very high income. However the main problem is related to finding the right balance between income and investment in this area in order to guarantee the return of the latter in the future.

Cash Cows: These are business areas that have gained a relatively large market share in the past, but over time the growth of the respective industry has slowed markedly, the cash flow in this position is well balanced, since investment in such a business area requires the bare minimum. Such a business area can bring a good income to the organization (These are the former "Stars").

Problem Children: These business areas compete in growing industries but hold relatively small market share. This combination of circumstances leads to the need to increase investment in order to protect its market share. High growth rates require significant cash flow to match this growth.

"Dogs": These are business areas with relatively small market share in slow growing industries. Cash flow is negligible, sometimes even negative.

But not many people use the Classic model, as it is impractical due to the need to obtain up-to-date data on the state of the market and the share occupied by the company and its competitor. Therefore, for calculations we use

Tailored Model:

The adapted BCG matrix is ​​built on the basis of the company's internal information. Required data - sales volumes of products for a certain period, which cannot be less than 12 months, in the future, to track the dynamics, it is necessary to add data for the next 3 months (i.e. data for 12, 15, 18, 21, 24 months) . The data does not have to start from the month of January, but must be by month. It is also important to consider the seasonality of sales of goods or services for your company's products. In the company under consideration, the commodity portfolio consists of 5 groups of goods, and there is also data on their sales for the period January - December 2013.

Table 5. Sales data of NordWest LLC

– multiplying the weight by the assessment and summing the obtained values ​​for all factors, we get a weighted assessment / market attractiveness rating

Table 7. Evaluation of the attractiveness of the industry

Table 8. Assessment of the competitive position in the industry

2 .Building the McKinsey Matrix for Nord-West LLC

On the x-axis we set aside 3.6 points, on the y-axis we set aside 2.9 points. At the intersection of these scores, we fall into the "Success 3" square. Which is inherent in organizations whose market attractiveness is kept at an average level, but at the same time their advantages in this market are obvious and strong. The strategic conclusions from the analysis based on the McKinsey matrix are clear: Nord-West LLC "falls into the "Success 3" square

Rice. 4. McKinsey matrix

The “success 3” position is characterized by the highest degree of market attractiveness and relatively strong advantages in it. The enterprise will be the undisputed leader or one of the leaders in the construction market, and the threat to it can only be the strengthening of some positions of individual competitors. Therefore, the strategy of an enterprise that is in such a position should be aimed at protecting its condition in the majority with the help of additional investments. Organizations need to first identify the most attractive market segments and invest in them, develop their advantages and resist the influence of competitors.


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Course of lectures on discipline

"Matrix Analysis"

for 2nd year students

Faculty of Mathematics specialty

"Economic cybernetics"

(lecturer Dmitruk Maria Aleksandrovna)

1. Function definition.

Df. Let

is a scalar argument function. It is required to define what is meant by f(A), i.e. we need to extend the function f(x) to the matrix value of the argument.

The solution to this problem is known when f(x) is a polynomial:

, Then .

The definition of f(A) in general case.

Let m(x) be the minimal polynomial A and have the canonical decomposition

, , are the eigenvalues ​​of A. Let the polynomials g(x) and h(x) take the same values.

Let g(A)=h(A) (1), then the polynomial d(x)=g(x)-h(x) is the annihilating polynomial for A, since d(A)=0, hence d(x ) divided by linear polynomial, i.e. d(x)=m(x)*q(x) (2).

, i.e. (3), , , .

Let us agree on m numbers for f(x) such

call the values ​​of the function f(x) on the spectrum of the matrix A, and the set of these values ​​will be denoted by .

If the set f(Sp A) is defined for f(x), then the function is defined on the spectrum of the matrix A.

It follows from (3) that the polynomials h(x) and g(x) have the same values ​​on the spectrum of the matrix A.

Our reasoning is reversible, i.e. from (3) Þ (3) Þ (1). Thus, if the matrix A is given, then the value of the polynomial f(x) is completely determined by the values ​​of this polynomial on the spectrum of the matrix A, i.e. all polynomials g i (x) that take the same values ​​on the spectrum of the matrix have the same matrix values ​​g i (A). We require that the definition of the value of f(A) in the general case obey the same principle.

The values ​​of the function f(x) on the spectrum of the matrix A must fully determine f(A), i.e. functions having the same values ​​on the spectrum must have the same matrix value f(A). Obviously, to determine f(A) in the general case, it suffices to find a polynomial g(x) that would take the same values ​​on the spectrum A as the function f(A)=g(A).

Df. If f(x) is defined on the spectrum of the matrix A, then f(A)=g(A), where g(A) is a polynomial that takes the same values ​​on the spectrum as f(A),

Df.The value of the function from the matrix A we call the value of the polynomial in this matrix for

.

Among the polynomials from С[x], which take the same values ​​on the spectrum of the matrix A, as f(x), of degree not higher than (m-1), which takes the same values ​​on the spectrum A, as f(x) is the remainder of the division any polynomial g(x) having the same values ​​on the spectrum of the matrix A as f(x) to the minimal polynomial m(x)=g(x)=m(x)*g(x)+r(x) .

This polynomial r(x) is called the Lagrange-Sylvester interpolation polynomial for the function f(x) on the spectrum of the matrix A.

Comment. If the minimal polynomial m(x) of matrix A has no multiple roots, i.e.

, then the value of the function on the spectrum .

Example:

Find r(x) for arbitrary f(x) if the matrix

. Let us construct f(H 1). Find the minimal polynomial H 1 - the last invariant factor :

, d n-1 = x 2 ; d n-1 =1;

m x \u003d f n (x) \u003d d n (x) / d n-1 (x) \u003d x nÞ 0 – n-fold root of m(x), i.e. n-fold eigenvalues ​​of H 1 .

, r(0)=f(0), r’(0)=f’(0),…,r (n-1) (0)=f (n-1) (0)Þ .


2. Properties of functions from matrices.

Property #1. If the matrix

has eigenvalues ​​(there may be multiples among them), and , then the eigenvalues ​​of the matrix f(A) are the eigenvalues ​​of the polynomial f(x): .

Proof:

Let the characteristic polynomial of matrix A have the form:

, , . Let's count. Let's move from equality to determinants:

Let's make a change in equality:

(*)

Equality (*) is valid for any set f(x), so we replace the polynomial f(x) by

, we get: .

On the left, we have obtained the characteristic polynomial for the matrix f(A), decomposed on the right into linear factors, which implies that

are the eigenvalues ​​of the matrix f(A).

CHTD.

Property #2. Let the matrix

and are the eigenvalues ​​of the matrix A, f(x) is an arbitrary function defined on the spectrum of the matrix A, then the eigenvalues ​​of the matrix f(A) are .

Proof:

Because function f(x) is defined on the spectrum of the matrix A, then there exists an interpolation polynomial of the matrix r(x) such that

, and then f(A)=r(A), and the matrix r(A) will have eigenvalues ​​according to property No. 1 which will be respectively equal to .

It makes it possible to determine the optimal sequence for studying the subjects included in the curriculum. Each subject in the curriculum has its own number.

Let the curriculum include 19 subjects. We build a square matrix with a base, which is equal to the number of subjects in the curriculum (19).

The method of expert assessment by experienced teachers determines the most significant relationships between academic subjects. The columns of the matrix are considered consumers, and the rows are considered information carriers. For example, for column 10 important bearers information are lines 7, 9, 11, that is, knowledge on subjects with these numbers. These rows in the column are reflected by ones (1), the absence of a cash connection - by zeros (0). As a result of the analysis, a matrix of the nineteenth order was formed. The analysis of the matrix consists in the sequential removal of columns and rows. Columns filled with zeros do not receive information from other subjects, that is, their study is not based on a logical relationship with other subjects, although they, in turn, can be carriers of primary information. This means that subjects that have numbers in these columns can be studied first. Lines filled with zeros are not considered information carriers and will not be the basis for studying other subjects, which means they can be studied last.

First, columns 7,8, 9,18 and their corresponding rows are crossed out. We get the first reduced matrix of the fifteenth order, which in turn has zero columns 4, 16, 17. Getting rid of them, we get the second reduced matrix. Having thus carried out all subsequent reductions, we obtain a matrix in which there are no columns without ones, but there are zero rows, which are also crossed out along with their corresponding columns. Having successively performed similar actions, we arrive at a matrix of this form, as shown in the diagram.

The formed matrix corresponds to the graph shown in Figure 3.2. This graph contains three closed double contours (13-15), (5-6), (11-10). With some approximation, we can assume that the subjects that entered these circuits should be studied in parallel, and first subjects with numbers 13 and 15 are studied, and only then subjects 5, 6, 10, 11.

As a result of the conducted matrix analysis, it becomes possible to create a schematic (block) model of the study of subjects in the curriculum:

The diagram shows a combined system for connecting educational subjects. The cells contain the numbers of subjects with parallel study. An educated connection system should be understood not as a mandatory sequence of connecting one group of subjects only after the end of the previous one, but only as a need to get ahead in their study. It only indicates a general trend in the connection of objects.

Matrix Analysis Program

Allows you to evaluate the logical sequence of the location educational material within the subject and improve it accordingly.

Let the subject include 6 topics. Matrix A! compiled according to the thematic plan of this academic subject. The numbers of topics that, when compiling the matrix, are considered in terms of their use in the study of other topics are arranged vertically, the numbers located horizontally correspond to the topics considered in terms of their use of information from other topics.

To identify closed loops, the presence of which indicates the impossibility of establishing the passage of the sequence of passage of individual topics, we carry out transformations (shortening) of the matrix Au. We delete row 5, consisting of zeros, and the column corresponding to it, as well as the zero column 3 with the corresponding row. Matrix A2 is formed.

The matrix A2 has missing rows and columns consisting of only zeros. To establish closed contours, we present the graph corresponding to the matrix A2 (see Fig. 3.3, a).

From the study of the graph, it follows that the presence of closed contours is caused by the relationship between the content of the educational material of topics 1 and 6, as well as topics 4 and 6. The reason for the noted relationship is the unsuccessful redistribution of the content of the educational material between these topics. After reviewing the content of these topics, it becomes possible to eliminate the existing closed contours of the graph. Thus, a new graph is formed (Fig. 3.3, b) and the corresponding matrix A3.

Reducing this matrix gives a new matrix A4.

After removing the arcs (6, 4), (6, 1) and (1, 6), we obtain a new initial matrix B1, the graph of which has no closed contours.

Now that the loops are broken, let's start adjusting the order of the topics. To do this, we will sequentially delete columns consisting of zeros and rows of the same name with them. Topics in these columns do not use information from other topics and can therefore be explored first.

In the matrix! columns 1 and 3 are null. Thus, topic 1 can take its place in the thematic plan. When examining the reasons for putting Topic 3 before Topic 2, it turns out that some of the information on Topic 2 takes place in Topic 3. However, it is more logical and more useful to leave them in Topic 3.

After rearranging the educational material, instead of the arc (3, 2) we get the arc (2, 3); delete column 1 - we get the matrix B2.

We assign the former number 2 to topic 2. Delete column 2 row 2. We get matrix B3.

Themes 3 and 4 remain with the same numbers. Delete columns 3, 4 with the corresponding rows; we get the matrix B4

Topic 6 is assigned number 5, and topic 5 is number 6.

We compose matrix C1 according to the new distribution of topics.

Let's carry out transformations of the matrix, sequentially deleting zero rows and columns with the same name. We move the topics corresponding to them to the end of the row, because the information of these topics is not used in the study of other topics. Topic 5 is assigned the number 6.

Delete row and column 6. Assign topic 6 number 5.

We delete lines 4 and 3 and the topics that answer them, assign the former numbers 4 and 3.

For topics 1 and 2, the same numbers remain in the thematic plan. As a result of the matrix processing, the following final arrangement of topics in the structure of the subject is obtained:

It can be seen from the above sequence that after matrix processing of the structure thematic plan topics 5 and 6 have swapped places. In addition, it became necessary to move the educational material on topic 5 to topic 1, as well as from topic 2 to topic 3.

As can be seen from the above example, the matrix analysis of the structure of the educational material makes it possible to streamline and improve it to a certain extent. mutual arrangement curriculum topics.

It should be noted that matrix analysis curricula and programs requires from the performers a lot of practical experience and a deep knowledge of the content of the training. First of all, this refers to the compilation of the initial matrix, more precisely, to the definition of links between academic subjects or learning topics inside the subject. There are many connections between such large elements as program topics, but matrix analysis performers must be able to "read between the lines" (find hidden but real connections), determine the significance of various connections in relation to the goals of matrix analysis, and sometimes be critical of the content of the topics of educational subjects.