SEARCH MATHEMATICA 8 DOCUMENTATION

THIS IS DOCUMENTATION FOR AN OBSOLETE PRODUCT.
SEE THE DOCUMENTATION CENTER FOR THE LATEST INFORMATION.

Mathematica > Mathematics and Algorithms > Matrices and Linear Algebra > Matrix Operations >

Built-in Mathematica Symbol

Inverse

Inverse[m]
gives the inverse of a square matrix m.

For matrices with approximate real or complex numbers, the inverse is generated to the maximum possible precision given the input. A warning is given for ill-conditioned matrices.

Inverse[m, ZeroTest->test] evaluates test[m[[i, j]]] to determine whether matrix elements are zero. The default setting is ZeroTest->(#0&).

Inverse of a 2×2 matrix:

Enter the matrix in a grid:

Inverse of a symbolic matrix:

Inverse of a 2×2 matrix:

Enter the matrix in a grid:

Inverse of a symbolic matrix:

Exact inverse of a Hilbert matrix:

Plot the imaginary parts of a Vandermonde matrix for a discrete Fourier transform:

Plot the inverse of a matrix, shading according to absolute value:

Show positive entries as black and others as white:

The inverse may not exist:

Typically a pseudo inverse does:

Full inverses do not exist for rectangular matrices:

Accurate inverses cannot be found for ill-conditioned machine-precision numerical matrices:

Exact result:

Arbitrary-precision result: