power

Scilab Function
Last update : 13/01/2005

power - power operation `(^,.^)`

### Calling Sequence

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

### Parameters

- `A,t`: scalar, polynomial or rational matrix.
- `b`:a scalar, a vector or a scalar matrix.

### Description

  - `"(A:square)^(b:scalar)"` : If `A` is a square matrix and `b` is a scalar then `A^b` is the matrix `A` to the power `b`.
  - `"(A:matrix).^(b:scalar)"` : 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` (elementwise power). If `A` is a vector and `b` is a scalar then `A^b` and `A.^b` performs the same operation (i.e elementwise power).
  - `"(A:scalar).^(b:matrix)"` 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))`.
  - `"(A:matrix).^(b:matrix)"` 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`,