matrix power

How much of your life can you fit into rows in columns? Well, enough of it for you to cherish the matrix as a valuable organizational and analytical tool.

Spreadsheets, tables, and matrices are used in every aspect of life. We track finances, monitor tasks, plan our future, and analyze potential relationships with rows and columns. And we are surrounded by this information as individuals, as part of small social groups, and as part of large organizations such as classes, companies, or governments.

More simply, matrices and tables give a new structure to elements of our life that are not always so two-dimensional. From the new structure, we can glean new insights and inspire new visualization of those same elements to make best-informed decisions. To me, a matrix is a valuable analytical tool that helps organize information for insight and action.

(Note that I am using the term “matrix” to represent that much more than numerical arrays of the math world. I am including categorical mappings, tables, lists, and spreadsheets too.)

The University of Cambridge Institute for Manufacturing nicely defines the matrix as an essential decision support tool:
  

“A two by two matrix is a useful tool for initial sorting of qualitative data. The axes should be chosen so that, e.g., the data with the most desirable characteristics will fall into the upper left quadrant and the least desirable in the lower right quadrant. While groups may be unable or unwilling to assign absolute values to qualitative data, they usually find it relatively easy to come to a consensus as to which quadrant something belongs in.

Generally, the two by two matrix is a useful tool for categorising things that can be reduced to two simple variables, particularly when quantitative information is unavailable and qualitative judgments must be made.

It enables a rapid clustering (or separating) of information into four categories, which can be defined to suit the purpose of the exercise. It is particularly useful with groups as a way of visibly plotting out a common understanding or agreement of a subject.”

Authors Alex Lowy and Phil Hood describe the matrix as “the most flexible and portable weapon in the knowledge worker’s intellectual arsenal”.

What’s best about the matrix is that flexibility. Depending on need, you can get as much power out of a 2×2 matrix as you can from a 5×5 matrix. Increased dimension does not translate to increased power. The matrix is flexible and dynamic to the needs of your analysis. You control the path to discovery.

And although matrices do a nice job of pairing categorical relationships, you can also translate these pairs to numerous other visualizations to better contextualize the information at hand. Turn your row and column headers into scaled concepts, map them to some x- and y- axes, and try and fit your qualitative information to a line that describes the relationship between x and y. Is the relationship directly proportional, inversely proportional, linear, parabolic, or along some other path? What do each of these types of relationships mean for your categorical variables?

It’s important to note that there can be fuzzy lines too. Not all cells need to have values and not all relationships need any sort of defined continuity. Empty cells and undefined relationships provide insights that are just as valuable as the populated and defined ones. Lack of data is data in itself, and that’s a great thing.

In the end, the matrix is just one part of the analytical toolbox and can provide a wide range of insight for your personal and professional life. Box up your data, organize it, visualize it, and use new structure to optimize your life.

Examples

Business/Leadership: Gartner, an IT research and advisory company, has created the “Magic Quadrant” to analyze types of entities in the business world. By plotting the ability (or inability) to execute against the completeness (or incompleteness) of vision, businesses can be categorized with those sharing similar characteristics, as Leaders, Challengers, Visionaries and Niche Players. This is a useful example of turning abstract qualities into groups for targeted strategy and decision making.

Product Development/Management: For analyzing how to grow a business from the product side, one matrix shows how plotting types of markets vs types of products can help guide that growth strategy.

Math/Statistics: Type I and Type II error tables are used to describe possible errors made in a statistical decision process. This is a great example of mapping relationships between categories, naming the cells, and using the matrix to understand what each cell represents.

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