If you give a matrix with exact symbolic or numerical entries, Mathematica
gives the exact inverse. If, on the other hand, some of the entries in your matrix are approximate real numbers, then Mathematica
finds an approximate numerical result.
When you try to invert a matrix with exact numerical entries, Mathematica
can always tell whether or not the matrix is singular. When you invert an approximate numerical matrix, Mathematica
can usually not tell for certain whether or not the matrix is singular: all it can tell is, for example, that the determinant is small compared to the entries of the matrix. When Mathematica
suspects that you are trying to invert a singular numerical matrix, it prints a warning.
If you work with high-precision approximate numbers, Mathematica
will keep track of the precision of matrix inverses that you generate.
works only on square matrices. "Advanced Matrix Operations"
discusses the function PseudoInverse
, which can also be used with nonsquare matrices.