expm

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