# power

(^,.^) power operation

## Calling Sequence

    t=A^b
                t=A**b
                t=A.^b

## Arguments

A,t

  scalar, polynomial or rational matrix.

b

  a scalar, a vector or a scalar matrix.

## Description

- If `A` is a square matrix and `b` is a scalar then `A^b` is the matrix `A` to the power `b`.

- If `b` is a scalar and `A` a matrix then `A.^b` is the matrix formed by the element of `A` to the power `b` (element-wise power). If `A` is a vector and `b` is a scalar then `A^b` and `A.^b` performs the same operation (i.e. element-wise power).

- If `A` is a scalar and `b` is a matrix (or vector) `A^b` and `A.^b` are the matrices (or vectors) formed by `a^(b(i,j))`.

- If `A` and `b` are vectors (matrices) of the same size `A.^b` is the `A(i)^b(i)` vector (`A(i,j)^b(i,j)` matrix).

Notes:

- For square matrices `A^p` is computed through successive matrices multiplications if `p` is a positive integer, and by diagonalization if not.

- `**` and `^` operators are synonyms.

## Examples

    A=[1 2;3 4];
    A^2.5,
    A.^2.5
    (1:10)^2
    (1:10).^2

    s=poly(0,'s')
    s^(1:10)

## See Also

- exp
- hat