Book B

Table of Contents

1. Chapter 1 — Introduction
2. Chapter 2 — Vectors
3. Chapter 3 — Linear Transformations

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A linear system is a mathematical model used to describe relationships between variables that obey the principle of superposition.¹

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.

1. This definition originates from classical linear algebra texts. ↩