The exponential of a square matrix (eM).

Syntax

e = MatExp(M)

Arguments

Name

Description

M

A square matrix.

Outputs

Name

Description

e

The exponential of the matrix.

Example

Find the exponential of the matrix [1, 2; 3, 4].

Syntax

e = MatExp([1, 2; 3, 4])

Results

[Matrix] 2 x 2

   51.969      74.737

    112.1      164.07

Comments

The matrix exponential extends the Maclaurin series of the exponential function ex to a square matrix argument.  So, for a matrix A, eA = I + A + A2/2 + … + An/n! …
The matrix exponential is useful in solving certain systems of ordinary differential equations.