       Eigensystem

• To: mathgroup at smc.vnet.net
• Subject: [mg39671] Eigensystem
• From: Angela Birk <angela.birk at hwwa.de>
• Date: Fri, 28 Feb 2003 04:46:32 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```Dear MathGroup Members,

I would like to generate a 12x12 matrix for that I can caluclate the
Eigensystem by transposing a 12x12 matrix. This 12x12 matrix is the
result of a model that includes a bunch of functions and variables.
(Note the attached file doesn't work, because the model is missing. But
one can see that the mistake occurs.)
[contact the author to get the attachment - moderator]

I try to derive the 12x12 matrix by using different commands:

First, I define the first row of the matrix (see attached file):

f[a_,b_] := f[a,b]=Table[(1-CDF[h[a,bValue,W]])*
SETP[bValue,b[[i]]]*ATP[a, j] + CDF[h[a,bValue,W]]*
SETP[bValue,b[[i]]]*ATP[a, j], {j, 1, 4}, {i, 1,3}]

where CDF[h[a,bValue,W]] is a probability that depends on the function h
and SETP[bValue,b[[i]]] as well as ATP[a, j] are given matrices having
the dimensions 3x3 and 4x4, respectively.

Second, if I execute the command

f[1, b[]] // MatrixForm

this should give a 1x12 vector. But actually I get a 4x3 matrix (see
attached file). This 1x12 vector is the first row of the 12x12 matrix,
and the sum of row is one. (Each row has to sum to one.)

Could someone suggest how the above command(s) should be changed to get
the 1x12 vector that sums to one?

Third, after having the vector, I'd like to generate the 12x12 matrix
with the following command

Table[f[a,b[[k]]], {a, 1, 4}, {k, 1, 3}] // MatrixForm

But actually this gives a 4x3x4x3 matrix (see attached file).

Fourth, if I transpose the above matrix and try to calculate the
Eigensystem, I get the failure message (see attached file).

I think, the mistake has something to do with the Table command. Does
somebody know, how I have to change the commands to get the desired
results?

Thank's in advance for the help.

Angela

--
Angela Birk
University of Hamburg
HWWA
20347 Hamburg, Germany
+49 40 42834 - 478

```

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