mpower: Matrix Power

In matlib: Matrix Functions for Teaching and Learning Linear Algebra and Multivariate Statistics

Matrix Power

Description

A simple function to demonstrate calculating the power of a square symmetric matrix in terms of its eigenvalues and eigenvectors.

Usage

mpower(A, p, tol = sqrt(.Machine$double.eps))

Arguments

A	a square symmetric matrix
p	matrix power, not necessarily a positive integer
tol	tolerance for determining if the matrix is symmetric

Details

The matrix power p can be a fraction or other non-integer. For example, p=1/2 and p=1/3 give a square-root and cube-root of the matrix.

Negative powers are also allowed. For example, p=-1 gives the inverse and p=-1/2 gives the inverse square-root.

Value

A raised to the power p: A^p

See Also

The {%^%} operator in the expm package is far more efficient

Examples

C <- matrix(c(1,2,3,2,5,6,3,6,10), 3, 3) # nonsingular, symmetric
C
mpower(C, 2)
zapsmall(mpower(C, -1))
solve(C)    # check

matlib documentation built on Oct. 3, 2024, 1:09 a.m.