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<!DOCTYPE MAN SYSTEM "../../manrev.dtd">
<MAN>
  <LANGUAGE>eng</LANGUAGE>
  <TITLE>householder</TITLE>
  <TYPE>Scilab Function</TYPE>
  <DATE>April 1993</DATE>
  <SHORT_DESCRIPTION name="householder"> Householder orthogonal reflexion matrix</SHORT_DESCRIPTION>
  <CALLING_SEQUENCE>
    <CALLING_SEQUENCE_ITEM>u=householder(v [,w])  </CALLING_SEQUENCE_ITEM>
  </CALLING_SEQUENCE>
  <PARAM>
    <PARAM_INDENT>
      <PARAM_ITEM>
        <PARAM_NAME>v</PARAM_NAME>
        <PARAM_DESCRIPTION>
          <SP>: real or complex column vector</SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>
      <PARAM_ITEM>
        <PARAM_NAME>w</PARAM_NAME>
        <PARAM_DESCRIPTION>
          <SP>: real or complex column vector with same size as <VERB>v</VERB>. Default value is <VERB>eye(v)</VERB></SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>
      <PARAM_ITEM>
        <PARAM_NAME>u</PARAM_NAME>
        <PARAM_DESCRIPTION>
          <SP>: real or complex column vector</SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>
    </PARAM_INDENT>
  </PARAM>
  <DESCRIPTION>
    <P>
    given 2 column vectors <VERB>v</VERB>, <VERB> w</VERB> of same size, <VERB>householder(v,w)</VERB> returns a unitary 
    column vector <VERB>u</VERB>, such that <VERB> (eye()-2*u*u')*v</VERB> is proportional to <VERB>w</VERB>.
    <VERB>(eye()-2*u*u')</VERB> is the orthogonal Householder reflexion matrix .</P>
    <P><VERB>w</VERB> default value is <VERB> eye(v)</VERB>. In this case vector <VERB> (eye()-2*u*u')*v</VERB> is the 
    vector  <VERB> eye(v)*norm(v)</VERB>.</P>
  </DESCRIPTION>
  <SEE_ALSO>
    <SEE_ALSO_ITEM>
      <LINK>qr</LINK>
    </SEE_ALSO_ITEM>
    <SEE_ALSO_ITEM>
      <LINK>givens</LINK>
    </SEE_ALSO_ITEM>
  </SEE_ALSO>
</MAN>
