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## Re: fishy rank

**From**: |
Etienne Grossmann |

**Subject**: |
Re: fishy rank |

**Date**: |
Thu, 17 May 2001 09:31:06 +0100 |

**User-agent**: |
WEMI/1.13.7 (Shimada) FLIM/1.13.2 (Kasanui) Emacs/20.7 (i386-debian-linux-gnu) (with unibyte mode) |

Hello,
From: Daniel Heiserer <address@hidden>
# I have situations where
# :rank(A)>rank([A,B]);
# also
# :rank(A)>=rank(A^n)
# if n is large enough.
[snip]
# Can this be seen as a numerical problem in
# terms of conditioning?
Could be because
(singular values of A^n) == (sing. vals. of A).^2
so that the ratio of small/big sing. val. will tend to zero. If A
has all sing. vals. equal to zero or one, there is no problem (see
below).
Cheers,
Etienne
======================================================================
octave:23> A = randn (5,3); [U,D,V] = svd (A,"cheap"); A = U*U';
octave:24> rA = rank (A)
rA = 3
octave:25> for i = 1:100:1000, if rank (A^i) != rA, [i, rank (A^i)], end; end
octave:26> A = randn (5,3); A = A*A';
octave:27> rA = rank (A)
rA = 3
octave:28> for i = 1:10:100, if rank (A^i) != rA, [i, rank (A^i)], end; end
ans =
21 2
ans =
31 1
ans =
41 1
ans =
51 1
ans =
61 1
ans =
71 1
ans =
81 1
ans =
91 1
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-------------------------------------------------------------

**Re: system command**, *(continued)*
**Re: system command**, *Paul Kienzle*, `2001/05/17`
**Re: system command**, *Jan-Mark Batke*, `2001/05/17`
**Re: system command**, *John W. Eaton*, `2001/05/17`
**Re: system command**, *John W. Eaton*, `2001/05/17`
**test if octave is running**, *Jan-Mark Batke*, `2001/05/28`
**Re: test if octave is running**, *Paul Kienzle*, `2001/05/28`
**remove fields from structure**, *Jan-Mark Batke*, `2001/05/31`
**Re: system command**, *Paul Kienzle*, `2001/05/17`
**Re: system command**, *Jan-Mark Batke*, `2001/05/17`

**Re: fishy rank**, *Paul Kienzle*, `2001/05/17`
**Re: fishy rank**,
*Etienne Grossmann* **<=**