Matrix Notation

Matrices are usually denoted by a capital letter and elements are arranged in a grid-like fashion, surrounded by brackets or parentheses (similar to vectors).

Here is an example of a $3 \times 3$ matrix $A$:

This matrix could also be written as

but the first option (with the brackets) is more common in engineering-related fields.

I will be using brackets for the rest of the course.

Size of a Matrix

As I have already mentioned above, this is a $3 \times 3$ matrix. The first $3$ refers to the number of rows, the second $3$ to the number of columns. A matrix does not have to have the same amount of rows and columns, for instance, we could define a matrix $A$ as follows:

and this would be a $2 \times 3$ matrix.

A matrix where the number of rows is the same as the number of columns (as in the first example) is called a square matrix. A matrix where the number of rows is different from the number of columns (as in the last example) is called a rectangular matrix.

A $3 \times 3$ matrix is said to be a “three by three” matrix.