matrixcalc (version 1.0-3)

matrix.power: 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

Value

An order \(n\) matrix.

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.

References

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

Examples

# NOT RUN {
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 )
# }