A test matrix is a matrix chosen to assess the accuracy, robustness, or performance of a numerical algorithm. Known eigenvalues, singular values, inverses, or deliberately difficult features make such examples useful for checking methods in numerical analysis (Higham 1991, 1995). The designation describes a use, while a structured matrix is specified by relations among its entries.
The following gallery compares six families. Each graphic demonstrates a particular numerical feature; the sizes and parameters are specified in the individual definitions. The examples test different problems, so a difficult eigenvalue computation need not imply the same difficulty when solving a linear system of equations.
| diagnostic | matrix | feature illustrated |
| Lotkin matrix | singular-value decay,  |
| Frank matrix | eigenvalue sensitivity,  |
| Kahan matrix | diagonal estimate versus smallest singular value |
| Grcar matrix | pseudospectral contours,  |
| Forsythe matrix | eigenvalue displacement,  |
| Wilkinson matrix | close eigenvalue pairs,  |
