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Subject: Re: How to figure 'matrix coupling' out?
Date: Sat, 14 Apr 2012 05:44:27 +0000 (UTC)
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"flying" wrote in message <jmar84$2ah$1@newscl01ah.mathworks.com>...
> Hi,everyone!I have a question for you.
> I have two 4x4 complex matrices.
> 
> Ar =  1.2485 + 0.1236i   0.0320 - 0.1570i   0.0245 + 0.0153i   0.0184 - 0.0097i
>     -0.0041 - 0.1868i   0.8390 + 0.5215i   0.1207 + 0.0593i  -0.0008 + 0.1226i
>     -0.0604 - 0.0353i   0.0097 - 0.1781i   0.1500 + 0.9788i   0.0425 - 0.0036i
>     0.0172 - 0.0026i  -0.0864 + 0.0996i  -0.0423 - 0.0094i   0.9084 + 0.3718i
> 
> Ac =  0.8987 + 0.6650i   0.0302 - 0.0282i  -0.0035 + 0.0219i  -0.0146 - 0.0581i
>       0.0328 - 0.0334i   0.7194 + 0.6143i   0.1217 + 0.1499i  -0.0790 + 0.1035i
>      -0.0215 - 0.0325i   0.1310 - 0.2428i  -0.4942 + 0.8434i  -0.0291 + 0.0318i
>       0.0256 - 0.0727i  -0.1420 + 0.0203i   0.0053 + 0.0046i   0.6475 + 0.7799i
> 
> I want to reorder their eigenvalues.First,i do eigenvalue decomposition of 
> matrix 'Ar'signing as 'lambdaAr'.It is a vector.
> 
> lambdaAr =   [1.2190 + 0.0767i 0.9510 + 0.3090i 0.8505 + 0.6179i 0.1253 + 0.9921i];
> lambdaAc =   [-0.5358 + 0.8443i 0.5878 + 0.8090i 0.8941 + 0.6496i 0.8254 + 0.5997i];
> 
> My question is that i want to reorder matrix Ac's eigenvalues 'lambdaAc' corresponding to the order of 'lambdaAr'.
> Maybe it is a question of 'matrix coupling'.
> How can i do?Please do me a favor everybody.Thank you very much!
- - - - - - - - -
  The two sets of eigenvalues of Ar and Ac are perfectly arbitrary, depending as they do on the complex contents of these matrices, so in effect you are asking how to reorder one arbitrary set of four points in the complex plane so as to best "correspond" to another arbitrary set of four.

  Can you describe what you would like to see in such a correspondence?  I can think of criteria such as to minimize the sum of the Euclidean distances between corresponding pairs, or perhaps the sum of the squares of these distances.  There must be many ways of finding a "best" correspondence among the 24 possibilities, but it is up to you to tell us what it is you want in this respect.  We can't read your mind.

Roger Stafford