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`_ element-wise exponential
+ `hat`_ (^) exponentiation


.. _hat: hat.html
.. _exp: exp.html