### Introduction

A matrix norm is a number defined in terms of the entries of the matrix. The norm is a useful quantity which can give important information about a matrix.

#### Prerequisites

- be familiar with matrices and their use in writing systems of equations
- revise material on matrix inverses, be able to find the inverse of a $2\times 2$ matrix, and know when no inverse exists
- revise Gaussian elimination and partial pivoting
- be aware of the discussion of ill-conditioned and well-conditioned problems earlier in Section 30.1

#### Learning Outcomes

- calculate norms and condition numbers of small matrices
- adjust certain systems of equations with a view to better conditioning

#### Contents

1 Matrix norms1.1 The 1-norm

1.2 The infinity-norm

1.3 The Euclidean norm

1.4 Other norms

2 Condition numbers

2.1 Condition numbers and conditioning