Introduction to Matrices - 3D Math Primer for Graphics and Game Development - page 114

This section presents matrices from a purely mathematical perspective.
It is divided into eight subsections.

• Section 4.1.1 introduces the concept of matrix dimension and de-

scribes some matrix notation.

• Section 4.1.2 describes square matrices.

• Section 4.1.3 interprets vectors as matrices.

• Section 4.1.4 describes matrix transposition.

• Section 4.1.5 explains how to multiply a matrix by a scalar.

• Section 4.1.6 explains how to multiply a matrix by another matrix.

• Section 4.1.7 explains how to multiply a vector by a matrix.

• Section 4.1.8 compares and contrasts matrices for row and column

vectors.

4.1.1 Matrix Dimensions and Notation

Just as we defined the dimension of a vector by counting how many numbers
it contained, we will define the size of a matrix by counting how many rows
and columns it contains. We say that a matrix with r rows and c columns
is an r × c (read “r by c”) matrix. For example, a 4 × 3 matrix has 4 rows
and 3 columns:

2
4 4

3
5

0 12

√

−5 4 3

A 4 × 3 matrix

.

12 −4/3 −1

1/2 18 0

This 4 × 3 matrix illustrates the standard notation for writing matrices:
the numbers are arranged in a grid enclosed by square brackets. Note
that some authors may enclose the grid of numbers with parentheses rather
than brackets, and other authors use straight vertical lines. We reserve
this last notation for an entirely separate concept related to matrices, the
determinant of a matrix. (We discuss determinants in Section 6.1.)
As we mentioned in Section 2.1, in this topic we represent a matrix
variable with uppercase letters in boldface, for example, M , A , R . When
we wish to refer to the individual elements within a matrix, we use subscript
notation, usually with the corresponding lowercase letter in italics. This is
shown below for a 3 × 3 matrix: