Linear Algebra with Applications, 10th Edition

Generating Matrices

We can also generate by matrices using built-in MATLAB functions. For example, the command

$$B=\mathsf{\text{rand}}\left(4\right)$$

will generate a $4\times 4$ matrix whose entries are random numbers between 0 and 1. Other functions that can be used to generate matrices are eye, zeros, ones, magic, hilb, pascal, toeplitz, compan, and vander. To build triangular or diagonal matrices, we can use the MATLAB functions triu, tril, and diag.

The matrix building commands can be used to generate blocks of partitioned matrices. For example, the MATLAB command

$$E=\left[\begin{array}{c}\mathsf{\text{eye}}\left(\mathrm{2}\right),\mathsf{\text{ones}}\left(\mathrm{2}\mathrm{,}\mathrm{3}\right);\mathsf{\text{zeros}}\left(\mathrm{2}\right),\left[1:3;3:-1:1\right]\end{array}\right]$$

will generate the matrix

$$\begin{array}{c}\hfill E=\\ 1\hfill & 0\hfill & 1\hfill & 1\hfill & 1\hfill \\ 0\hfill & 1\hfill & 1\hfill & 1\hfill & 1\hfill \\ 0\hfill & 0\hfill & 1\hfill & 2\hfill & 3\hfill \\ 0\hfill & 0\hfill & 3\hfill & 2\hfill & 1\hfill \end{array}$$