expm

Matrix exponential

Syntax

R = expm(A)

R = expm(A) computes the matrix exponential of the square matrix A.

Compute the matrix exponential for the 2-by-2 matrix and simplify the result.

syms x
A = [0 x; -x 0];
simplify(expm(A))

ans =
[  cos(x), sin(x)]
[ -sin(x), cos(x)]

Input matrix, specified as a square symbolic matrix.

Resulting function, returned as a symbolic matrix.

The matrix exponential e^A of matrix A is

$e^{A} = \sum_{k = 0}^{\infty} \frac{1}{k!} A^{k} = 1 + A + \frac{A^{2}}{2} + \dots$