A symmetric matrix is one where the elements either side of the diagonal mirror one another. That is Mi,j = Mj,i, or, in other words, M is the matrix transpose of itself.
An example 3 x 3 symmetric matrix:
| 3 | -1 | 2 |
| -1 | 7 | 1 |
| 2 | 1 | -3 |
Used in Chap. 7: pages 91, 101
Also known as symmetric matrices