Identifying Types of Matrices

By Mary Jane Sterling

A matrix is a useful structure that you can use in a variety of finite math problems to change the format of mathematical statements to make them more usable and understandable.

A matrix is nothing more (or nothing less) than a rectangular arrangement of numbers or letters or other items. You can use matrices to organize data by month, person, age group, company, and so on. You then use that information to make decisions and solve problems.

Matrices come in all sorts of sizes, but their shapes are always the same: They are rectangular arrays of objects called elements of a matrix. The rectangular arrays can be as small as 1 × 1 and as large as you can handle on a spreadsheet or on your wall! They can be square, such as 2 × 2 or rectangular, such as 4 × 7.
Their size is called their dimension.

The dimension of a matrix is indicated with R × C where R is the number of rows in the matrix and C is the number of columns.

When a matrix has the same number of rows as columns, then it’s a square matrix. Matrices with just one row are called row matrices, and those with only one column are column matrices. This figure shows a sampling of matrices, different ways of identifying them, and their respective dimensions.

FinitMath-matrix-sampler
Matrix sampler.

You’re probably wondering what good a zero matrix can do you. It really does come in handy when you need a target of “nothing left” or if you want to subtract a matrix to create opposites.

Identity matrices are always square matrices. They can be 2 × 2, 3 × 3, 4 × 4, and so on.

Their characteristic is in having a diagonal of 1s and all 0s otherwise. Identity matrices play a huge role in the work with matrix applications.