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<!DOCTYPE MAN SYSTEM "../../manrev.dtd">
<MAN>
  <LANGUAGE>eng</LANGUAGE>
  <TITLE>equil</TITLE>
  <TYPE>Scilab Function</TYPE>
  <DATE>April 1993</DATE>
  <SHORT_DESCRIPTION name="equil"> balancing of pair of symmetric matrices</SHORT_DESCRIPTION>
  <CALLING_SEQUENCE>
    <CALLING_SEQUENCE_ITEM>T=equil(P,Q)  </CALLING_SEQUENCE_ITEM>
  </CALLING_SEQUENCE>
  <PARAM>
    <PARAM_INDENT>
      <PARAM_ITEM>
        <PARAM_NAME>P, Q</PARAM_NAME>
        <PARAM_DESCRIPTION>
          <SP>: two positive definite symmetric matrices</SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>
      <PARAM_ITEM>
        <PARAM_NAME>T</PARAM_NAME>
        <PARAM_DESCRIPTION>
          <SP>: nonsingular matrix</SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>
    </PARAM_INDENT>
  </PARAM>
  <DESCRIPTION>
    <P><VERB>equil</VERB> returns <VERB>t</VERB> such that:</P>
    <P><VERB>T*P*T'</VERB> and  <VERB>inv(T)'*Q*inv(T)</VERB>  are both equal to a same 
    diagonal and positive matrix.</P>
  </DESCRIPTION>
  <EXAMPLE>
<![CDATA[
P=rand(4,4);P=P*P';
Q=rand(4,4);Q=Q*Q';
T=equil(P,Q)
clean(T*P*T')
clean(inv(T)'*Q*inv(T))
 ]]>
  </EXAMPLE>
  <SEE_ALSO>
    <SEE_ALSO_ITEM>
      <LINK>equil1</LINK>
    </SEE_ALSO_ITEM>
    <SEE_ALSO_ITEM>
      <LINK>balanc</LINK>
    </SEE_ALSO_ITEM>
    <SEE_ALSO_ITEM>
      <LINK>ctr_gram</LINK>
    </SEE_ALSO_ITEM>
  </SEE_ALSO>
</MAN>
