MATLAB was originally designed for linear algebra computations, so it not surprising that it has a rich set of functions for solving linear equation and eigenvalue problems. Many of the linear algebra functions are based on routines from the LAPACK [3] Fortran library.

Most of the linear algebra functions work for both real and complex matrices. We write A* for the conjugate transpose of A. Recall that a square matrix A is Hermitian if A* = A and unitary if A* A = I, where I is the identity matrix. To avoid clutter, we use the appropriate adjectives for complex matrices. Thus, when the matrix is real, "Hermitian" can be read as "symmetric" and "unitary" can be read as "orthogonal". For background on numerical linear algebra see [13], [21], [73] or [75].

9.1 Norms and Condition Numbers

A norm is a scalar measure of the size of a vector or matrix. The p-norm of an n-vector x is defined by

For p = ? the norm is defined by

The norm function can compute any p-norm and is invoked as norm(x, p), with default p = 2. As a special case, for p = ?inf the quantity min _i x _i is computed. Example:

  <span class="unicode">?</span> x = 1:4;  <span class="unicode">?</span> [norm (x, 1) norm (x, 2) norm (x, inf) norm (x, -inf)]  ans =...