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Inverse
Inverse[
m
] gives the inverse of a square matrix m.
Inverse works on both symbolic and numerical matrices.
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
,
Modulus->
n
] evaluates the inverse modulo n.
Inverse[
m
,
ZeroTest
->
test
] evaluates test
[
m
[[
i
,
j
]]
] to determine whether matrix elements are zero. The default setting is ZeroTest
->
(#
==
0
&).
A Method option can also be given. Possible settings are as for LinearSolve.
See the Mathematica book: Section 1.8.3, Section 3.7.6.
See also Implementation NotesA.9.44.27MainBookLinkOldButtonDataA.9.44.27, Implementation NotesA.9.44.29MainBookLinkOldButtonDataA.9.44.29.
See also: PseudoInverse, LinearSolve, RowReduce, NullSpace.
Related package: LinearAlgebra`Tridiagonal`.
Further Examples
The inverse of a 2 x 2 matrix displayed as a matrix.
In[1]:= 
Out[1]//MatrixForm= 
If the matrix is singular, the inverse is not computed.
In[2]:= 
Inverse::sing: Matrix {{1, 3}, {2, 6}} is singular.
Out[2]= 
If the matrix is not square, the inverse is not computed.
In[3]:= 
Inverse::matsq: Argument {{1, 2, 2}, {3, 1, 4}} at position 1 is not a square matrix.
Out[3]= 
You can compute inverse of inexact matrices.
In[4]:= 
Out[4]//MatrixForm= 
Here is the inverse over the integers modulo 5.
In[5]:= 
Out[5]//MatrixForm= 
This checks the result.
In[6]:= 
Out[6]//MatrixForm= 
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