A matrix is symmetric if the transpose of the matrix is itself (i.e., A = A' ). In other words, the lower triangle of the square matrix is a "mirror image" of the upper triangle (see below).

|1 2 3 4|

|2 1 5 6|

|3 5 1 7|

|4 6 7 1|

For more information on matrices, see Matrix Ill-Conditioning, Matrix Inverse, Matrix Rank, and Matrix Singularity.