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

## Description

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

## Usage

 `1` ```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`

The `{%^%}` operator in the expm package is far more efficient
 ```1 2 3 4 5``` ```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 ```