# mpower

From matlib v0.9.2
by Michael Friendly

##### Matrix Power

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

```
# NOT RUN {
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
# }
```

*Documentation reproduced from package matlib, version 0.9.2, License: GPL (>= 2)*

### Community examples

Looks like there are no examples yet.