Path: news.mathworks.com!not-for-mail
From: <HIDDEN>
Newsgroups: comp.soft-sys.matlab
Subject: Re: finding a matrix used in matrix transformation
Date: Wed, 10 Nov 2010 17:36:05 +0000 (UTC)
Organization: Xoran Technologies
Lines: 29
Message-ID: <ibel65$al2$1@fred.mathworks.com>
References: <ibc1cs$61o$1@fred.mathworks.com> <ibc2ic$mjm$1@fred.mathworks.com> <ibc4lr$cjv$1@fred.mathworks.com> <ibcjtb$1nt$1@fred.mathworks.com> <ibckv4$8q2$1@fred.mathworks.com> <ibd3k2$8l3$1@fred.mathworks.com> <ibdhgb$k7j$1@fred.mathworks.com> <ibef50$130$1@fred.mathworks.com> <ibefk2$2hn$1@fred.mathworks.com> <ibehlj$ijd$1@fred.mathworks.com>
Reply-To: <HIDDEN>
NNTP-Posting-Host: webapp-05-blr.mathworks.com
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
X-Trace: fred.mathworks.com 1289410565 10914 172.30.248.35 (10 Nov 2010 17:36:05 GMT)
X-Complaints-To: news@mathworks.com
NNTP-Posting-Date: Wed, 10 Nov 2010 17:36:05 +0000 (UTC)
X-Newsreader: MATLAB Central Newsreader 1440443
Xref: news.mathworks.com comp.soft-sys.matlab:685603

"pushkarini " <pushkarini.a@gmail.com> wrote in message <ibehlj$ijd$1@fred.mathworks.com>...

Then, I thought, it is probably not possible to convert A into orth(A) using such a method in the first place? 
==============

Correct. The transformation B=inv(M)*A*M will cause B to have the same eigenvalues as A. But orth(A) in general will not have the same eigenvalues as A.


I guess, adding proper 'lengths' to the row vectors of the orthonormal basis will solve the problem? 
============

I don't know what this means, but it sounds doubtful.


> I am doing all this to convert my matrix A which I start with to a normal matrix (ie. whose eigenvectors are perpendicular to eachother).
====================

Always a good idea to say what you really want in the first place!!!

Assuming A has a full set of n eigenvalues, you can do the following

 
%Engine
[V,D]=eig(A);
iV=inv(V);

M=(V*V')^(.5);

B=inv(M)*A*M;