Services & Resources / Wolfram Forums
-----
 /
MathGroup Archive
2006
*January
*February
*March
*April
*May
*June
*July
*August
*September
*October
*November
*December
*Archive Index
*Ask about this page
*Print this page
*Give us feedback
*Sign up for the Wolfram Insider

MathGroup Archive 2006

[Date Index] [Thread Index] [Author Index]

Search the Archive

Matrix decomposition with NullSpace and QRDecomposit

  • To: mathgroup at smc.vnet.net
  • Subject: [mg64139] Matrix decomposition with NullSpace and QRDecomposit
  • From: Tobias Burnus <burnus at gmx.de>
  • Date: Thu, 2 Feb 2006 00:06:45 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

(Retried - this time w/o attachment; forget to de-attach it before
sending the mail - sorry.)

Hello,

I have a Hermitian matrix of the form

( A    B )
( B'   C ) =: M

(B' = Transpose[B]), of which I want to bring B (5×18) into this form
{D, O} =

 d11 d12 d13 d14 d15 0 0 0 0 0 0 0 0 0 0 0 0 0
 d21 d22 d23 d24 d25 0 0 0 0 0 0 0 0 0 0 0 0 0
 d31 d32 d33 d34 d35 0 0 0 0 0 0 0 0 0 0 0 0 0
 d41 d42 d43 d44 d45 0 0 0 0 0 0 0 0 0 0 0 0 0
 d51 d52 d53 d54 d55 0 0 0 0 0 0 0 0 0 0 0 0 0

where O should be zero. For a simple case I succeeded using
  Q = QRDecomposition[B]
  L = NullSpace[Transpose[B]],  (see below)
but it fails for a more complicated case - there not all (O)ij are zero.
(See http://www.physik.fu-berlin.de/~tburnus/tmp/MatrixDecomposition.nb )

This is with Mathematica 5.2.
It works if I set pds1=pds2=...=pds6 and pdp1=...pdp6.

Any ideas?

Besides, does anyone know a quick way to get D Hermitian, currently it
has triangular form.

Tobias

Excerpt from the notebook
--------
HC1 = (.... the matrix ...)
HC1C := HC1[[Range[1, 5], Range[6, 23]]]

Q = QRDecomposition[
        Transpose[HC1C]][[1]]
L = NullSpace[HC1C]
T = IdentityMatrix[Length[HC1]];

T[[Range[6, 6 + Length[Q] - 1],
      Range[6, Length[HC1]]]] = Q;
\!\(\(T\[LeftDoubleBracket]Range[6 + Length[Q], Length[HC1]],
        Range[6, Length[HC1]]\[RightDoubleBracket]\  = \

Table[L\[LeftDoubleBracket]i\[RightDoubleBracket]\/\@\(\(Conjugate[L]\)\
\[LeftDoubleBracket]i\[RightDoubleBracket] . L\[LeftDoubleBracket]i\
\[RightDoubleBracket]\), {i, 1, Length[L]}];\)\)

T=Assuming[
      pd\[Sigma]1<0&&pd\[Pi]1>0&&pd\[Sigma]2<0&&pd\[Pi]2>0&&pd\[Sigma]3<0&&
        pd\[Pi]3>0&&pd\[Sigma]4<0&&pd\[Pi]4>0&&pd\[Sigma]5<0&&pd\[Pi]5>0&&
        pd\[Sigma]6<0&&pd\[Pi]6>0,FullSimplify[T]];

myHC1 = T.HC1.Transpose[T] // FullSimplify



  • Prev by Date: Re: Trying to animate the rotation of a plane about an axis using dynamic visualizer - MoviePlot3D.nb (0/1)
  • Next by Date: Re: Trying to animate the rotation of a plane about an axis using dynamic visualizer - MoviePlot3D.nb (0/1)
  • Previous by thread: New MathCode Functionality Expands Options for Prototyping C++ and Fortran 90 Applications in Mathematica
  • Next by thread: Re: Matrix decomposition with NullSpace and QRDecomposit