Defining a matrix
Mathematicians define a matrix as simply a rectangular array that has m rows and n columns, like the one shown in the following screenshot:
Figure 2.2 – Model of a matrix with m rows and n columns
In math, matrices are written out a particular way. An example 4 × 5 matrix is shown in the following expression. Notice that it has four rows and five columns:
Figure 2.3 – Example of a 4 x 5 matrix
Notation
In math and quantum computing, matrix variable names are in capital letters, and each entry in a matrix is referred to by a lowercase letter that corresponds to the variable name with subscripts (aij). Subscript i refers to the row the entry is in and subscript j refers to the column it is in. The following formula shows this for a 3 × 3 matrix:
In our example matrix A, a22 = 1. What is a32? Hint—it's the only number that begins with the letter n.
