Introduction to Matrices - 3D Math Primer for Graphics and Game Development - page 113

Chapter 4

Introduction to Matrices

Unfortunately, no one can be told what the matrix is.
You have to see it for yourself.
— Morpheus in The Matrix (1999)

Matrices are of fundamental importance in 3D math, where they are primar-
ily used to describe the relationship between two coordinate spaces. They
do this by defining a computation to transform vectors from one coordinate
space to another.
This chapter introduces the theory and application of matrices. Our
discussion will follow the pattern set in Chapter 2 when we introduced
vectors: mathematical definitions followed by geometric interpretations.

• Section 4.1 discusses some of the basic properties and operations of

matrices strictly from a mathematical perspective. (More matrix op-
erations are discussed in Chapter 6.)

• Section 4.2 explains how to interpret these properties and operations

geometrically.

• Section 4.3 puts the use of matrices in this topic in context within

the larger field of linear algebra.

4.1 Mathematical Definition of Matrix

In linear algebra, a matrix is a rectangular grid of numbers arranged into
rows and columns. Recalling our earlier definition of vector as a one-
dimensional array of numbers, a matrix may likewise be defined as a two-
dimensional array of numbers. (The “two” in “two-dimensional array”
comes from the fact that there are rows and columns, and should not be
confused with 2D vectors or matrices.) So a vector is an array of scalars,
and a matrix is an array of vectors.

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