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<!DOCTYPE MAN SYSTEM "../../manrev.dtd">
<MAN>
  <LANGUAGE>eng</LANGUAGE>
  <TITLE>power</TITLE>
  <TYPE>Scilab Function</TYPE>
  <DATE>April 1993</DATE>
  <SHORT_DESCRIPTION name="power"> power operation <VERB>(^,.^)</VERB>   </SHORT_DESCRIPTION>
  <CALLING_SEQUENCE>
    <CALLING_SEQUENCE_ITEM>t=A^b</CALLING_SEQUENCE_ITEM>
    <CALLING_SEQUENCE_ITEM>t=A**b</CALLING_SEQUENCE_ITEM>
    <CALLING_SEQUENCE_ITEM>t=A.^b</CALLING_SEQUENCE_ITEM>
  </CALLING_SEQUENCE>
  <PARAM>
    <PARAM_INDENT>
      <PARAM_ITEM>
        <PARAM_NAME>A,t</PARAM_NAME>
        <PARAM_DESCRIPTION>
          <SP>: scalar, polynomial or rational matrix.</SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>
      <PARAM_ITEM>
        <PARAM_NAME>b</PARAM_NAME>
        <PARAM_DESCRIPTION>
          <SP>:a scalar, a vector or a scalar matrix.</SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>
    </PARAM_INDENT>
  </PARAM>
  <DESCRIPTION>
    <ITEMIZE>
      <ITEM> <SP><VERB>"(A:square)^(b:scalar)"</VERB>
        : If <VERB>A</VERB> is a square matrix and <VERB>b</VERB> is a scalar then  <VERB>A^b</VERB> is the matrix <VERB>A</VERB> to the power <VERB>b</VERB>.</SP>
      </ITEM>
      <ITEM> <SP><VERB>"(A:matrix).^(b:scalar)"</VERB>
    : If <VERB>b</VERB> is a scalar and <VERB>A</VERB> a matrix then
    <VERB>A.^b</VERB>  is the matrix formed by the element of
    <VERB>A</VERB> to the power <VERB>b</VERB> (elementwise power). If
    <VERB>A</VERB> is a vector and <VERB>b</VERB> is a scalar then
    <VERB>A^b</VERB> and <VERB>A.^b</VERB> performs the same operation
    (i.e elementwise power). </SP>
      </ITEM>
      <ITEM> <SP><VERB>"(A:scalar).^(b:matrix)"</VERB>
        If <VERB>A</VERB> is a scalar  and <VERB>b</VERB> is a matrix (or vector) <VERB>A^b</VERB> and <VERB>A.^b</VERB> are the matrices (or vectors) formed by  <VERB> a^(b(i,j))</VERB>.</SP>
      </ITEM>
      <ITEM> <SP><VERB>"(A:matrix).^(b:matrix)"</VERB>
        If <VERB>A</VERB> and <VERB>b</VERB>  are vectors (matrices) of the same size <VERB>A.^b</VERB> is the  <VERB>A(i)^b(i)</VERB> vector (<VERB>A(i,j)^b(i,j)</VERB> matrix).</SP>
      </ITEM>
    </ITEMIZE>
    <P>
    Notes:</P>
    <P>
     -
    For square matrices <VERB>A^p</VERB> is computed through successive
    matrices multiplications if <VERB>p</VERB> is a positive integer, and by
    diagonalization if not.</P>
    <P>
     -
    <VERB>**</VERB> and <VERB>^</VERB> operators are synonyms.</P>
  </DESCRIPTION>
  <EXAMPLE>
<![CDATA[
A=[1 2;3 4];
A^2.5,
A.^2.5
(1:10)^2
(1:10).^2

s=poly(0,'s')
s^(1:10)
 ]]>
  </EXAMPLE>
  <SEE_ALSO>
    <SEE_ALSO_ITEM>
      <LINK>exp</LINK>
    </SEE_ALSO_ITEM>
  </SEE_ALSO>
</MAN>
