← Back to branch summary

~ubuntu-branches/ubuntu/hoary/scilab/hoary

« back to all changes in this revision

Viewing changes to man/eng/linear/spanplus.xml

  • Committer: Bazaar Package Importer
  • Author(s): Torsten Werner
  • Date: 2005-01-09 22:58:21 UTC
  • mfrom: (1.1.1 upstream)
  • Revision ID: james.westby@ubuntu.com-20050109225821-473xr8vhgugxxx5j
Tags: 3.0-12
http://bugs.debian.org/255869
changed configure.in to build scilab's own malloc.o, closes: #255869

Show diffs side-by-side

added added

removed removed

Lines of Context:
man/eng/linear/spanplus.xml
 
1
<?xml version="1.0" encoding="ISO-8859-1" standalone="no"?>
 
2
<!DOCTYPE MAN SYSTEM "../../manrev.dtd">
 
3
<MAN>
 
4
  <LANGUAGE>eng</LANGUAGE>
 
5
  <TITLE>spanplus</TITLE>
 
6
  <TYPE>Scilab Function</TYPE>
 
7
  <DATE>April 1993</DATE>
 
8
  <SHORT_DESCRIPTION name="spanplus"> sum of subspaces</SHORT_DESCRIPTION>
 
9
  <CALLING_SEQUENCE>
 
10
    <CALLING_SEQUENCE_ITEM>[X,dim,dima]=spanplus(A,B[,tol])   </CALLING_SEQUENCE_ITEM>
 
11
  </CALLING_SEQUENCE>
 
12
  <PARAM>
 
13
    <PARAM_INDENT>
 
14
      <PARAM_ITEM>
 
15
        <PARAM_NAME>A, B</PARAM_NAME>
 
16
        <PARAM_DESCRIPTION>
 
17
          <SP>: two real or complex matrices with equal number of rows</SP>
 
18
        </PARAM_DESCRIPTION>
 
19
      </PARAM_ITEM>
 
20
      <PARAM_ITEM>
 
21
        <PARAM_NAME>X</PARAM_NAME>
 
22
        <PARAM_DESCRIPTION>
 
23
          <SP>: orthogonal or unitary square matrix</SP>
 
24
        </PARAM_DESCRIPTION>
 
25
      </PARAM_ITEM>
 
26
      <PARAM_ITEM>
 
27
        <PARAM_NAME>dim, dima</PARAM_NAME>
 
28
        <PARAM_DESCRIPTION>
 
29
          <SP>: integers, dimension of subspaces</SP>
 
30
        </PARAM_DESCRIPTION>
 
31
      </PARAM_ITEM>
 
32
      <PARAM_ITEM>
 
33
        <PARAM_NAME>tol</PARAM_NAME>
 
34
        <PARAM_DESCRIPTION>
 
35
          <SP>: nonnegative real number</SP>
 
36
        </PARAM_DESCRIPTION>
 
37
      </PARAM_ITEM>
 
38
    </PARAM_INDENT>
 
39
  </PARAM>
 
40
  <DESCRIPTION>
 
41
    <P>
 
42
    computes a  basis X such that:</P>
 
43
    <P>
 
44
    the first <VERB>dima</VERB> columns of <VERB>X</VERB> span Range(<VERB>A</VERB>)
 
45
    and the following (<VERB>dim-dima</VERB>) columns make a basis of <VERB>A+B</VERB>
 
46
    relative to <VERB>A</VERB>.</P>
 
47
    <P>
 
48
    The <VERB>dim</VERB> first columns of <VERB>X</VERB> make a basis for <VERB>A+B</VERB>.</P>
 
49
    <P>
 
50
    One has the following canonical form for <VERB>[A,B]</VERB>:</P>
 
51
    <VERBATIM>
 
52
<![CDATA[
 
53
         [*,*]    (dima rows)
 
54
X'*[A,B]=[0,*]    (dim-dima rows)
 
55
         [0,0]    
 
56
   ]]>
 
57
    </VERBATIM>
 
58
    <P><VERB>tol</VERB> is an optional argument (see function code).</P>
 
59
  </DESCRIPTION>
 
60
  <EXAMPLE>
 
61
<![CDATA[
 
62
A=rand(6,2)*rand(2,5);      // rank(A)=2
 
63
B=[A(:,1),rand(6,2)]*rand(3,3);   //two additional independent vectors
 
64
[X,dim,dimA]=spanplus(A,B);
 
65
dimA
 
66
dim
 
67
 ]]>
 
68
  </EXAMPLE>
 
69
  <SEE_ALSO>
 
70
    <SEE_ALSO_ITEM>
 
71
      <LINK>spaninter</LINK>
 
72
    </SEE_ALSO_ITEM>
 
73
    <SEE_ALSO_ITEM>
 
74
      <LINK>im_inv</LINK>
 
75
    </SEE_ALSO_ITEM>
 
76
    <SEE_ALSO_ITEM>
 
77
      <LINK>spantwo</LINK>
 
78
    </SEE_ALSO_ITEM>
 
79
  </SEE_ALSO>
 
80
  <AUTHOR>F. D.; ;   </AUTHOR>
 
81
</MAN>