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 "Schur" method can be specified with method options mopts by Method->{"Schur",mopts}. The following method options can be given:
  • "Balanced"Falsewhether to balance the input matrix before doing the Schur decomposition
    "BlockSeparationDelta"Automaticmaximum 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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Scope  (8)

Generalizations & Extensions  (3)

Options  (2)

Applications  (3)

Properties & Relations  (6)

Possible Issues  (6)

Neat Examples  (1)

See Also

MatrixExp  MatrixLog  MatrixPower  Inverse  JordanDecomposition  Eigensystem  SchurDecomposition

Tutorials

Introduced in 2012
(9.0)