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expm

square matrix exponential

Syntax

expm(X)

Arguments

X

a square matrix with real or complex entries.

Description

If X is a square matrix then expm(X) is the matrix

expm(X) = I + X + X^2 /2 + ...

The computation is performed by first block-diagonalizing X and then applying a Pade approximation on each block.

Padé approximant is the "best" approximation of a function by a rational function of given order. The technique was developed by Henri Padé, a French mathematician.

Examples

X=[1 2;3 4]
expm(X)
logm(expm(X))

See also

  • logm — square matrix logarithm
  • bdiag — block diagonalization, generalized eigenvectors
  • coff — resolvent (cofactor method)
  • log — natural logarithm
  • exp — element-wise exponential
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Last updated:
Mon Nov 07 14:58:51 CET 2022