Matrix notation and the size of a matrix

Matrices are used in a variety of different math settings from algebra and linear algebra to finite math. Of course, to be able to work with matrices, you need to understand the notation used and simple (but important) ideas like the size of a matrix.


Elements of a matrix

A matrix is a way of organizing numbers into rows and columns. It may represent a system of equations, a real-life situation, or simply be a matrix of interest all on its own. Matrices are most commonly labeled with capital letters such as A, B, or C. Below, you can see a matrix we will refer to as “matrix A“.


The numbers within the matrix, are referred to as elements. One way to talk about a specific element is to use a lowercase letter and label it with the row and column of the element.


Note that you could also say “5 is the (1,2) entry” and “8 is the (2,3) entry”.

The size of a matrix

The common theme with matrices is “think rows-columns”, and this holds even when discussing the size or dimension of a matrix. If a matrix has 4 rows and 6 columns, we say it is a 4 x 6 matrix (read: four by six).



As you study matrices, remember the following ideas:

  • Elements are referred to by their location in terms of the row, then column.
  • The size of a matrix is: (number of rows) x (number of columns). For a 2 x 3 matrix, you would say “the size of the matrix is 2 by 3”.

Continue studying matrices

Now that you have reviewed important notation and ideas like the size of a matrix, you are ready to study how to add, subtract, and multiply matrices.

Operations with matrices: