# 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 SchurParlett 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 "Schur" 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

# Examples

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## Basic Examples(2)

Compute the matrix sine and cosine of a 3×3 matrix m:

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Test the matrix identity :

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Compute a matrix polynomial, specifying the polynomial as a pure function:

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