# matrix.power: Matrix Raised to a Power In matrixcalc: Collection of functions for matrix calculations

## Description

This function computes the k-th power of order n square matrix x If k is zero, the order n identity matrix is returned. argument k must be an integer.

## Usage

 `1` ```matrix.power(x, k) ```

## Arguments

 `x` a numeric square matrix `k` a numeric exponent

## Details

The matrix power is computed by successive matrix multiplications. If the exponent is zero, the order n identity matrix is returned. If the exponent is negative, the inverse of the matrix is raised to the given power.

## Value

An order n matrix.

## Author(s)

Frederick Novomestky fnovomes@poly.edu

## References

Bellman, R. (1987). Matrix Analysis, Second edition, Classics in Applied Mathematics, Society for Industrial and Applied Mathematics.

## Examples

 ```1 2 3 4 5 6``` ```A <- matrix( c ( 1, 2, 2, 1 ), nrow=2, byrow=TRUE) matrix.power( A, -2 ) matrix.power( A, -1 ) matrix.power( A, 0 ) matrix.power( A, 1 ) matrix.power( A, 2 ) ```

### Example output

```           [,1]       [,2]
[1,]  0.5555556 -0.4444444
[2,] -0.4444444  0.5555556
[,1]       [,2]
[1,] -0.3333333  0.6666667
[2,]  0.6666667 -0.3333333
[,1] [,2]
[1,]    1    0
[2,]    0    1
[,1] [,2]
[1,]    1    2
[2,]    2    1
[,1] [,2]
[1,]    5    4
[2,]    4    5
```

matrixcalc documentation built on May 2, 2019, 1:45 p.m.