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 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