MatrixLog
MatrixLog[m]
gives the matrix logarithm of a matrix m.
Details and Options
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- 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
open allclose allScope (4)
Options (1)
Method (1)
Eigenvalues with relatively very small magnitude are treated as zero:
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Use Tolerance->0 to include nonzero eigenvalues of any magnitude:
Applications (1)
Properties & Relations (2)
If m is a nonsingular numeric matrix, then MatrixExp[MatrixLog[m]] is effectively equal to m:
But it is not always true for symbolic matrices:
Possible Issues (3)
MatrixLog does not work with singular matrices:
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The method "Jordan" can work with exact and inexact matrices:
The method "Schur" works only with inexact matrices:
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Neat Examples (1)
Text
Wolfram Research (2012), MatrixLog, Wolfram Language function, https://reference.wolfram.com/language/ref/MatrixLog.html.
CMS
Wolfram Language. 2012. "MatrixLog." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/MatrixLog.html.
APA
Wolfram Language. (2012). MatrixLog. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/MatrixLog.html