http://www.mathworks.com/matlabcentral/newsreader/view_thread/243131
MATLAB Central Newsreader  Matrix decomposition in vectors
Feed for thread: Matrix decomposition in vectors
enus
©19942014 by MathWorks, Inc.
webmaster@mathworks.com
MATLAB Central Newsreader
http://blogs.law.harvard.edu/tech/rss
60
MathWorks
http://www.mathworks.com/images/membrane_icon.gif

Mon, 26 Jan 2009 15:28:02 +0000
Matrix decomposition in vectors
http://www.mathworks.com/matlabcentral/newsreader/view_thread/243131#624003
Umair Mansoor
Can someone tell me how can I decompose a matrix in vectors, like, a 2x2 matrix in to the product of a 2x1 and 1x2 vectors?

Mon, 26 Jan 2009 16:11:04 +0000
Re: Matrix decomposition in vectors
http://www.mathworks.com/matlabcentral/newsreader/view_thread/243131#624020
John D'Errico
"Umair Mansoor" <umairbinmansoor@hotmail.com> wrote in message <glkkq2$8i2$1@fred.mathworks.com>...<br>
> Can someone tell me how can I decompose a matrix in vectors, like, a 2x2 matrix in to the product of a 2x1 and 1x2 vectors?<br>
<br>
In general, this is impossible, unless the 2x2 matrix<br>
is singular. For higher dimensioned matrices, the<br>
matrix must be rank 1 to be decomposed in this way.<br>
<br>
So is your 2x2 matrix singular? I.e., is it a rank 1 matrix?<br>
<br>
John

Mon, 26 Jan 2009 16:18:02 +0000
Re: Matrix decomposition in vectors
http://www.mathworks.com/matlabcentral/newsreader/view_thread/243131#624024
someone
"Umair Mansoor" <umairbinmansoor@hotmail.com> wrote in message <glkkq2$8i2$1@fred.mathworks.com>...<br>
> Can someone tell me how can I decompose a matrix in vectors, like, a 2x2 matrix in to the product of a 2x1 and 1x2 vectors?<br>
<br>
A = [1 2 3 ; 4 5 6]<br>
<br>
x1 = A(1,:)<br>
x2 = A(2,:)<br>
% etc.<br>
<br>
y1 = A(:,1)<br>
y2 = A(:,2)<br>
% etc.

Mon, 26 Jan 2009 17:51:01 +0000
Re: Matrix decomposition in vectors
http://www.mathworks.com/matlabcentral/newsreader/view_thread/243131#624051
Roger Stafford
"Umair Mansoor" <umairbinmansoor@hotmail.com> wrote in message <glkkq2$8i2$1@fred.mathworks.com>...<br>
> Can someone tell me how can I decompose a matrix in vectors, like, a 2x2 matrix in to the product of a 2x1 and 1x2 vectors?<br>
<br>
To decompose any matrix in the way you propose, use the singular value decomposition function, 'svd'. If there is only one nonzero singular value, then that gives you a solution. If there are more than one, no solution is possible.<br>
<br>
If the matrix is A, do<br>
<br>
[U,S,V] = svd(A);<br>
<br>
Suppose the only nonzero value in S is S(1,1). Then you have<br>
<br>
A = U*S*V' = (U(:,1)*S(1,1)) * (V(:,1)')<br>
<br>
which gives you a solution and shows you that the choice is only arbitrary up to a multiplicative constant. Otherwise no solution is possible.<br>
<br>
Roger Stafford

Tue, 27 Jan 2009 16:57:01 +0000
Re: Matrix decomposition in vectors
http://www.mathworks.com/matlabcentral/newsreader/view_thread/243131#624339
Umair Mansoor
"John D'Errico" <woodchips@rochester.rr.com> wrote in message <glknao$qv$1@fred.mathworks.com>...<br>
> "Umair Mansoor" <umairbinmansoor@hotmail.com> wrote in message <glkkq2$8i2$1@fred.mathworks.com>...<br>
> > Can someone tell me how can I decompose a matrix in vectors, like, a 2x2 matrix in to the product of a 2x1 and 1x2 vectors?<br>
> <br>
> In general, this is impossible, unless the 2x2 matrix<br>
> is singular. For higher dimensioned matrices, the<br>
> matrix must be rank 1 to be decomposed in this way.<br>
> <br>
> So is your 2x2 matrix singular? I.e., is it a rank 1 matrix?<br>
> <br>
> John<br>
<br>
I just know that its symmetric

Tue, 27 Jan 2009 17:55:03 +0000
Re: Matrix decomposition in vectors
http://www.mathworks.com/matlabcentral/newsreader/view_thread/243131#624359
John D'Errico
"Umair Mansoor" <umairbinmansoor@hotmail.com> wrote in message <glnect$80d$1@fred.mathworks.com>...<br>
> "John D'Errico" <woodchips@rochester.rr.com> wrote in message <glknao$qv$1@fred.mathworks.com>...<br>
> > "Umair Mansoor" <umairbinmansoor@hotmail.com> wrote in message <glkkq2$8i2$1@fred.mathworks.com>...<br>
> > > Can someone tell me how can I decompose a matrix in vectors, like, a 2x2 matrix in to the product of a 2x1 and 1x2 vectors?<br>
> > <br>
> > In general, this is impossible, unless the 2x2 matrix<br>
> > is singular. For higher dimensioned matrices, the<br>
> > matrix must be rank 1 to be decomposed in this way.<br>
> > <br>
> > So is your 2x2 matrix singular? I.e., is it a rank 1 matrix?<br>
> > <br>
> > John<br>
> <br>
> I just know that its symmetric<br>
<br>
If that is all you know, then it is impossible<br>
in general. It is not that we cannot find<br>
such a pair of vectors. Rather, there do not<br>
exist a pair of vectors such that this is true<br>
for a general 2x2 symmetric matrix.<br>
<br>
John