MatrixLog

MatrixLog[m]

gives the matrix logarithm of a matrix m.

Details and Options

  • MatrixLog is effectively the functional inverse of MatrixExp, so that MatrixExp[MatrixLog[m]] is m for a nonsingular matrix.
  • MatrixLog works only on square nonsingular matrices.
  • A Method option can be given, with possible explicit settings:
  • "Jordan"Jordan decomposition
    "Schur"Schur decomposition for inexact numerical matrices
  • The default setting of Method->Automatic uses the Schur decomposition for inexact numerical matrices and Jordan decomposition for exact and symbolic matrices.
  • The "Schur" method can also be specified by Method->{"Schur",Tolerance->tol}, where eigenvalues with a relative magnitude less than tol are effectively considered as 0 so that the matrix is considered as singular. Use Tolerance->0 to allow any nonzero eigenvalue, no matter how small.
  • MatrixLog works on SparseArray objects.

Examples

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Basic Examples  (1)

Logarithm of a 2×2 matrix:

In[1]:=
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Out[1]=
In[2]:=
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Out[2]=

Scope  (4)

Options  (1)

Applications  (1)

Properties & Relations  (2)

Possible Issues  (3)

Neat Examples  (1)

See Also

MatrixExp  MatrixPower  LinearSolve  Dot  SchurDecomposition  JordanDecomposition  Log  MatrixFunction

Introduced in 2012
(9.0)