Book A1

In Plain Sight 1

Chapter 0

Preface

Linear systems form the foundation of much of modern engineering and applied mathematics. This chapter introduces the basic concepts used throughout the text.

Figure 1.1 — Graph of the linear function $y = mx + b$.

I hear, I know; I see, I remember; I do, I understand.

Definition

A system is said to be linear if it satisfies additivity and homogeneity.

Theorem 1.1

Every linear transformation between finite-dimensional vector spaces can be represented by a matrix.

Example

The system y = 3x is linear, whereas y = x² is not.

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