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BUILT-IN MATHEMATICA SYMBOL
MatrixFunction
MatrixFunction[f, m]
gives the matrix generated by the scalar function f at the matrix argument m.
Details and Options
- A matrix function transforms a matrix to another matrix. For convergent power series, MatrixFunction[f, m] effectively evaluates the power series for the function f with ordinary powers replaced by matrix powers.
- The function f should be a unary differentiable or symbolic function.
- MatrixFunction works only on square matrices. It applies the Schur-Parlett method for inexact matrices and Jordan decomposition for exact or symbolic matrices.
- MatrixFunction can be used on SparseArray objects.
- A Method option can be given, with possible explicit settings:
-
"Jordan" Jordan decomposition "Schur" Schur decomposition with block Parlett recursion - The
method can be specified with method options mopts by Method->{"Schur", mopts}. The following method options can be given: -
"Balanced" False whether to balance the input matrix before doing the Schur decomposition "BlockSeparationDelta" Automatic maximum separation between adjacent eigenvalues in a single Parlett block
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