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Inverse

Inverse[m]
gives the inverse of a square matrix m.
MORE INFORMATION
  • 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, ZeroTest->test] evaluates to determine whether matrix elements are zero. The default setting is ZeroTest.
  • A Method option can also be given. Settings for exact and symbolic matrices include , , and . The default setting of Automatic switches among these methods depending on the matrix given.
EXAMPLESCLOSE ALL
Basic Examples   (3)
Inverse of a 2×2 matrix:
Enter the matrix in a grid:
Inverse of a symbolic matrix:
Inverse of a 2×2 matrix:
In[1]:=
Click for copyable input
Out[1]=
 
Enter the matrix in a grid:
In[1]:=
Click for copyable input
Out[1]=
 
Inverse of a symbolic matrix:
In[1]:=
Click for copyable input
Out[1]=
Applications   (3)
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:
Possible Issues   (3)
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:
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