What is matrix analysis? A comprehensive guide from the basics to practical application, even for beginners

Matrix analysis is a method of analyzing using two axes, vertical and horizontal, as perspectives.

By dividing into four segments for analysis, you can discover trends and biases in things that cannot be seen through normal listing.

Matrix analysis is a useful method, but some people may not have heard much about it.

Therefore, in this article, we will introduce the meaning of matrix analysis, analytical methods, and the benefits of using it.

In the latter half of the article, we will introduce how to create a matrix diagram, so please read until the end.

Basics of Matrix Analysis

Matrix analysis is an analytical method that arranges multiple elements or criteria vertically and horizontally, and classifies and evaluates items at their intersections.

Generally, 2x2 or 3x3 matrices are commonly used, but when there are many elements or when the situation is complex, more complex matrices may also be employed.

By utilizing matrix analysis, effects such as making complex information visually easier to understand and making it easier to identify the essence of problems in a simple manner can be expected.

Types of Matrix Analysis

Here, we will introduce four types of matrix analysis.

• L-type Matrix

• 4-Quadrant Matrix

• Mapping Matrix

• DMM

Let's take a detailed look at each type.

L-Type Matrix

An L-type matrix is a table where the vertical and horizontal axes are located at the outermost edges of the table.

It gets this name because the elements appear in the shape of the letter "L" in the alphabet.

Generally speaking, when people refer to a matrix, this is the type of table commonly seen.

It is used when analyzing two elements, with one element placed on the vertical axis of the table and the other on the horizontal axis.

<img width="516" height="87" alt="ac0efc64-b46d-4d31-953b-11dace33624d.png" src="null">

4-Quadrant Matrix

A 4-quadrant matrix is a chart with four areas created by two intersecting axes.

Since it allows for detailed analysis of matters, it is used for understanding problems and sharing issues within teams.

Note that using three axes for analysis actually makes it harder to analyze, so two axes are recommended.

Also, the top and bottom and left and right of the axes should contain opposite elements with low correlation. If you use elements with high correlation or the same elements, analysis becomes impossible.

<img width="561" height="116" alt="322e3ca0-7aeb-40bc-af80-f9eedefaec2c.png" src="null">

Mapping Matrix

A mapping matrix is a table where elements are arranged in areas divided into four sections by two axes.

For example, when conducting market analysis of business improvement tools, by setting the price range on the vertical axis and the richness of features on the horizontal axis, and placing tools that fall into the four areas, it helps to understand the differences in strategies and competitive relationships among each tool.

The advantage is that you can visually understand the distribution of each element.

<img width="372" height="123" alt="8f2a735d-deee-42f3-b1bb-e4f49ee3bdb3.png" src="null">

DMM

DMM (Diamond Mandala Matrix) is a table where you create a 3×3 matrix and arrange elements within it.

It is divided into 9 sections, with the function or subject being analyzed placed in the center, and the 8 surrounding areas are used for detailed analysis and subdivision.

Also called Mandala Chart (Mandalart), it became a topic of discussion when professional baseball player Shohei Ohtani was known to have used it during his high school years.

The method involves writing a goal such as "being selected as the first draft pick by 8 baseball teams" in the center, and then writing down what is necessary to achieve that goal in the surrounding areas.

It is effective for establishing a roadmap to achieve goals and understanding business functions, and is now widely adopted in educational settings and training programs.

Representative Matrix Analysis Methods

What has been introduced so far is merely methods for organizing information.

When it comes to utilizing information, the frameworks introduced from here on are used.

• SWOT Analysis

• Importance-Urgency Matrix

• PPM Analysis

• GE Matrix

• Ansoff's Growth Matrix

Let's take a detailed look at each of these methods.

SWOT Analysis

SWOT analysis is a framework used to understand the current state of a business or project.

First, it divides into two axes: the external environment surrounding the company, such as industry trends and competitors, and the internal environment, such as the company's brand power and quality.

Next, it is divided into four categories: "Strengths," "Weaknesses," "Opportunities," and "Threats," and each element is incorporated into these categories.

It is an effective framework when considering specific measures or making quick decisions.

Importance-Urgency Matrix

The Importance-Urgency Matrix is a framework for determining priorities in business and work tasks.

It was devised by Dwight D. Eisenhower, the 34th President of the United States, and is therefore also called the "Eisenhower Matrix".

Tasks are evaluated based on two elements: importance and urgency, and are classified into four areas: "important and urgent tasks," "important but not urgent," "not important but urgent," and "not important and not urgent."

This is a useful framework when reviewing resource allocation or when uncertain about work priorities.

PPM Analysis

PPM Analysis (Product Portfolio Management) is a framework for determining the allocation of management resources.

It enables an objective view of competitors and one's own business, making it useful for business decision-making.

It consists of two axes: market growth rate and market share, and classifies businesses into four areas: "Stars, Question Marks, Cash Cows, and Dogs".

• Stars: High in both market growth rate and market share

• Question Marks: High market growth rate with high future potential, but low market share

• Cash Cows: High market share, but low market growth rate

• Dogs: Low in both market growth rate and market share

On the other hand, since it cannot reflect all elements of a business, it may sometimes lead to incorrect management decisions.

It is also important to utilize other frameworks and consider the company's circumstances.

GE Matrix

The GE Matrix is a framework that divides businesses into nine types by classifying them as "high, medium, or low" on the vertical axis representing industry attractiveness and the horizontal axis representing business unit competitiveness.

If both industry attractiveness and business unit competitiveness are high, it becomes a target for investment.

However, if both industry attractiveness and business unit competitiveness are low, consideration must be given to reviewing or selling the business.

In summary, it is a framework useful for establishing business allocation and business strategy.

While the "PPM analysis" introduced earlier also exists, the GE Matrix's strength lies in its flexibility, as it incorporates factors such as the company's strengths and growth rates.

It is useful in situations where there are many elements that cannot be evaluated superficially, or in industries that change rapidly.

Ansoff's Growth Matrix

Ansoff's Growth Matrix is a framework based on two axes: "market" and "product," further divided into "existing" and "new."

It was proposed by a management scholar known as the father of strategic management.

Strategies can be classified into the following four types:

• Market Penetration Strategy (Existing Market × Existing Product): A strategy that aims to expand sales in existing markets with existing products

• Product Development Strategy (Existing Market × New Product): A strategy that aims to expand sales in existing markets with new products or services

• Diversification Strategy (New Market × New Product): A strategy that introduces new products or services into new markets

• Market Development Strategy (Existing Product × New Market): A strategy that aims to expand sales by introducing existing products into new markets

This is effective when management reaches an impasse or when aiming for business expansion.

Benefits of Conducting Matrix Analysis

Here, we will introduce the benefits of conducting matrix analysis.

The specific benefits are the following six:

• Ability to objectively grasp the position of things

• Ability to comprehensively identify and extract elements

• Easier to assign priorities and importance levels

• Ability to group elements

• Ability to convey complex information concisely

Let's look at each benefit.

Ability to Objectively Grasp the Position of Things

Matrix tables allow you to visually organize complex information, enabling you to objectively grasp the position of things.

By positioning elements based on established axes, you can understand aspects that would not be apparent from simply listing them.

For example, if you use a matrix diagram for work priorities, you can see at a glance the priority level and urgency of tasks.

Furthermore, because you can objectively understand the overall work situation, decision-making becomes smoother and problems become easier to identify.

Enables Comprehensive Identification of Elements

Matrix diagrams allow you to identify elements comprehensively without omissions by categorizing them based on vertical and horizontal axes.

While listing items tends to be subjective, matrix diagrams always make it clear what criteria are being used for classification through their axes, preventing any deviation or loss of objectivity.

Additionally, the axes of a matrix diagram function as a checklist, helping to prevent elements from being overlooked or missed.

Preventing the omission of elements leads to faster decision-making and business reviews.

Makes It Easier to Set Priorities and Importance Levels

By categorizing elements using a matrix diagram, you can visually understand their relative positioning, which allows you to identify which tasks are important and should be prioritized.

This prevents situations where team members are unsure "what to tackle first" when working on tasks together.

Additionally, it enables you to review appropriate personnel allocation and time distribution for tasks, which can also reduce the burden on employees themselves.

This is a significant benefit for companies as it leads to increased sales.

Elements Can Be Grouped

In matrix diagrams, it is possible to group elements.

When creating a diagram, you list out the elements and consider their placement based on axes, and during this process, you may discover some kind of relationship or commonality.

For example, elements with high relevance or similar elements tend to be placed close to each other on the matrix diagram.

Therefore, by grouping adjacent elements, it becomes easier to identify relationships and conduct analysis.

Of course, not all adjacent elements necessarily have a relationship, but there are connections that can only be discovered through the use of a matrix diagram.

Complex Information Can Be Conveyed Concisely

Since a matrix diagram itself is a very simple table, anyone can immediately grasp its content.

Matrix diagrams will be greatly helpful for communication that previously didn't work well for understanding situations.

When you understand things but find it difficult to further understand the underlying necessity or importance, use a matrix diagram.

Disadvantages of Matrix Analysis

While matrix analysis allows for objective understanding of situations and makes it easier to prioritize, it also has the following disadvantages:

• There is a possibility of overlooking important elements and information

• There is a possibility that the creator's intention may be misunderstood

• Experience is necessary for interpretation

Let's look at each of these disadvantages.

There is a possibility of overlooking important elements and information

Matrix diagrams simplify information as much as possible to make it easier to grasp, but in doing so, there is a possibility of cutting away even important elements that should be considered when making actual decisions.

For example, when reviewing or expanding a business, it is necessary to consider industry trends, economic impacts, political trends, and economic conditions, but it is difficult to read these from a matrix diagram alone.

While matrix diagrams are useful for grasping an overview, it is important to keep in mind that they may be oversimplified and important elements may have been removed when utilizing them.

There is a possibility that the creator's intention may be misunderstood

When comparing multiple tools or conducting matrix analysis of a company's strengths and weaknesses, it is common to use symbols such as "◎" (double circle), "○" (circle), "△" (triangle), and "×" (cross). However, if the definition of each symbol is not properly established, there is a possibility that the creator's intention may not be correctly conveyed.

For example, if the item "design quality of our company's service" is marked with "○", Person A might interpret it as sufficient, while Person B might perceive it as "since it's not ◎, it still needs improvement."

To ensure that the matrix you've created is used effectively, make sure to define in advance any content that might be interpreted differently depending on the viewer.

Experience is Required for Interpretation

Matrix diagrams allow you to visually grasp the positioning of information, but they are merely data.

To utilize them for business strategy or operational reviews, it is necessary to interpret the collected data.

Additionally, practical experience is required to communicate the analyzed data to third parties in an easy-to-understand manner.

How to Create a Matrix Diagram

Here, we will introduce how to create a matrix diagram divided into the following 6 steps:

• Decide the purpose of creating the matrix diagram

• Select the matrix type

• Determine the axes for arranging elements

• Write out and arrange the elements

• Decide the key message you want to convey through the matrix diagram

Let's look at each item in detail.

Determine the Purpose of Creating a Matrix Diagram

First, let's decide on the purpose of creating a matrix diagram.

While we simply call it a matrix diagram, this is a framework, and how to utilize it differs depending on the purpose.

For example, creating a matrix diagram can have the following purposes:

• Identify the priority and urgency of tasks to help review work operations

• Use as hints for future business ventures

• Review the allocation of management resources

Once the purpose is determined, you will understand which matrix diagram should be used.

If the purpose is not determined, the creation of the diagram will not proceed smoothly, so be sure to decide it in advance.

Choosing a Matrix Type

Next, let's choose a matrix type from the four types introduced.

• L-shaped Matrix: Recommended when comparing and analyzing four items

• 4-Quadrant Matrix: Recommended when you want to understand the characteristics and patterns of each item within the whole

• Mapping Matrix: Recommended when you want to grasp each element more visually

• DMM: Recommended when you want to establish a roadmap for achieving goals or understand business functions

Since each matrix type allows you to grasp different things, please choose according to your purpose.

Determine the axes for arranging elements

Next, let's decide on the items to set for the axes. Basically, you will decide on items based on your objectives and themes.

The specific decision-making process is as follows:

• Have the team share elements and conditions that form the basis of the theme

• Consolidate the shared conditions and select candidates according to the objective

• Next, select conditions that are polar opposites so that positions can be clearly identified

If there is overlap in the axes, the matrix diagram loses its meaning. Be sure to select items that are polar opposites or have low correlation.

Write Out and Arrange the Elements

Next, let's write out the elements.

If you can't think of the content, it's fine to fill it in roughly, so go ahead and fill it in.

In the first place, a matrix diagram is something where you compare multiple elements and notice commonalities and relationships from there.

Therefore, if you fill it in to a certain extent, the elements should naturally come to mind.

Determine the Key Message You Want to Convey Through the Matrix Diagram

Finally, decide on the key message you want to convey through the matrix diagram.

For matrix diagrams and graph creation in general, it is necessary to communicate the results through the process.

For example, think of important messages such as "We should focus on XX rather than XX business right now" or "Let's review the priorities of XX."

Summary

This article introduced matrix analysis and diagrams.

Matrix diagrams allow for visual comprehension of even complex information, making it possible to objectively understand one's position.

In business, there are various benefits such as activating communication among employees, which is important, proactive measures against potential risks, and enabling quick decision-making.

On the other hand, there are also disadvantages, such as the risk of overlooking important elements and detailed information, and the need for experience in interpretation.

That said, there are mostly significant benefits in business.

First, please try matrix analysis based on the content introduced in this article.