`funm`

Evaluates a general function of a square matrix.

Category: Mathematics > Linear Algebra

Syntax

F = funm(A, fun)

Returns fun applied to A as a matrix function, where fun is a function handle such as @exp.

Description

A function of a matrix is not the function applied to each entry. It is defined through the eigenstructure of A: for a diagonalizable A = V*D/V, f(A) = V*f(D)/V. funm computes it with the Schur form and works even when A is not diagonalizable.

For @exp it agrees with expm, and for @log with logm, but funm is less accurate than those dedicated functions.

Input arguments

A: Square matrix.
fun: Handle of a scalar function that also works elementwise, for example @exp, @sin or @sqrt.

Output arguments

F: Matrix of the same size as A.

Example

Matrix exponential through funm

A = [1 2; 0 3];
F = funm(A, @exp)
disp(norm(F - expm(A)) < 1e-10)

Output

F = 2×2

    2.7183   17.3673
         0   20.0855
   1

See also

expm logm sqrtm schur