# expm {Matrix}

### Description

Compute the exponential of a matrix.

### Usage

expm(x)

### Arguments

- x
- a matrix, typically inheriting from the
`dMatrix`

class.

### Details

The exponential of a matrix is defined as the infinite Taylor series `expm(A) = I + A + A^2/2! + A^3/3! + ...`

(although this is definitely not the way to compute it). The method for the `dgeMatrix`

class uses Ward's diagonal Pade' approximation with three step preconditioning.

### Values

The matrix exponential of `x`

.

### References

http://en.wikipedia.org/wiki/Matrix_exponential

Cleve Moler and Charles Van Loan (2003) Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later. *SIAM Review* **45**, 1, 3--49.

Eric W. Weisstein et al. (1999) *Matrix Exponential*. From MathWorld, http://mathworld.wolfram.com/MatrixExponential.html

### Note

The expm package contains newer (partly faster and more accurate) algorithms for `expm()`

and includes `logm`

and `sqrtm`

.

### Examples

Documentation reproduced from package Matrix, version 1.2-5. License: GPL (>= 2) | file LICENCE