powerplus (version 1.0)

Matpow: Matrix Power

Description

Raises any diagonalizable Matrix to any real power. Capabilities for non-diagonalizable matrices: Exponentiation (integer powers only), Square root

Usage

Matpow(M, numer, denom = 1)

Arguments

M

a square Matrix

numer

numerator of (rational) exponent. Can be a decimal number.

denom

denominator of rational exponent (1 by default)

Value

The solution to the exponentiation operation supplied. Computes a real-valued root whenever possible. Otherwise, the principal complex root.

Details

Method based on spectral decomposition. Allows to take powers and roots. Allows to compute the inverse matrix (if invertible).

References

For more on spectral decomposition (also known as eigendecomposition), visit http://mathworld.wolfram.com/EigenDecomposition.html

Examples

A <- matrix(1:4, ncol = 2)
Matpow(A, 3)
Matpow(A, 0.5)
Matpow(A, 0.2)
Matpow(A, 1, 5)
Matpow(A, 2, 4)
Matpow(A, -1)

C <- matrix(sample(1:1000, 81), ncol = 9)
Matpow(C, 2)
Matpow(C, 0.5)
Matpow(C, 4, 5)
Matpow(C, pi)
Matpow(C, 0.73)
Matpow(C, -1)

M <- matrix(c(1, 0, 1, 1), 2, 2)  # A non-diagonalizable matrix
Matpow(M, 3)
Matpow(M, 0.5)
Matpow(M, 4, 8)