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