R: Matrix Raised to a Power

matrix.power {matrixcalc} | R Documentation

## Matrix Raised to a Power

### 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

    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

    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 )

[Package matrixcalc version 1.0-3 Index]