MATLAB Function Reference
expm

Matrix exponential

Syntax

• ```Y = expm(X)
```

Description

```Y = expm(X) ``` raises the constant to the matrix power `X`. The `expm` function produces complex results if `X` has nonpositive eigenvalues.

Use `exp` for the element-by-element exponential.

Algorithm

`expm` is a built-in function that uses the Padé approximation with scaling and squaring. You can see the coding of this algorithm in the `expm1` demo.

 Note    The `expmdemo1`, `expmdemo2`, and `expmdemo3` demos illustrate the use of Padé approximation, Taylor series approximation, and eigenvalues and eigenvectors, respectively, to compute the matrix exponential.References [1] and [2] describe and compare many algorithms for computing a matrix exponential. The built-in method, `expm`, is essentially method 3 of [2].

Examples

This example computes and compares the matrix exponential of `A` and the exponential of `A`.

• ```A = [1        1        0
0        0        2
0        0       -1 ];

```expm(A)
```ans =
2.7183   1.7183        1.0862
0        1.0000        1.2642
0             0        0.3679

```exp(A)
```ans =
2.7183        2.7183        1.0000
1.0000        1.0000        7.3891
1.0000        1.0000        0.3679
```

Notice that the diagonal elements of the two results are equal. This would be true for any triangular matrix. But the off-diagonal elements, including those below the diagonal, are different.

`exp`, `funm`, `logm`, `sqrtm`