MATLAB Central Newsreader - variable help

variable help

Katie — Fri, 09 May 2008 16:05:05 -0400

This is my first time using MATLAB,
I am using this formula to compute sign patterns of 4x4
nilpotent matrices;
A(n+1)=P*A(n)*inv(P) for n=1,2,3,4, where P is a random
matrix and A(1) is the 4x4 jordan. (This formula can be
repeated up to n=4 before sign patterns are duplicated, n
is the number of times that the random matrix (P) can be
used- just a subscript to define the variables). so what I
did was:
A2=P*A1*inv(P)
A3=P*A2*inv(P)
A4=P*A3*inv(P)
A5=P*A4*inv(P)

I want to loop this until all the possible sign patterns
for nilpotent matrices are obtained, changing the random
matrix every 4 times. BUT obviously if I were to loop this
set of equations, for each new P the variables would just
be replaced each time since they are named the same. I have
tried using A(i) or A(n) like in the original equation, but
it is read as multiplication. How do I solve this problem?
or create some sort of subscript system so that the
subscript of the variables change each time.
THANK YOU!

Re: variable help

someone — Fri, 09 May 2008 16:30:18 -0400

Re: variable help

Roger Stafford — Fri, 09 May 2008 19:39:03 -0400

"Katie " <kmcdon03@uoguelph.ca> wrote in message <g01snh$q9j
$1@fred.mathworks.com>...
> This is my first time using MATLAB,
> I am using this formula to compute sign patterns of 4x4
> nilpotent matrices;
> A(n+1)=P*A(n)*inv(P) for n=1,2,3,4, where P is a random
> matrix and A(1) is the 4x4 jordan. (This formula can be
> repeated up to n=4 before sign patterns are duplicated, n
> is the number of times that the random matrix (P) can be
> used- just a subscript to define the variables). so what I
> did was:
> A2=P*A1*inv(P)
> A3=P*A2*inv(P)
> A4=P*A3*inv(P)
> A5=P*A4*inv(P)
>
> I want to loop this until all the possible sign patterns
> for nilpotent matrices are obtained, changing the random
> matrix every 4 times. BUT obviously if I were to loop this
> set of equations, for each new P the variables would just
> be replaced each time since they are named the same. I have
> tried using A(i) or A(n) like in the original equation, but
> it is read as multiplication. How do I solve this problem?
> or create some sort of subscript system so that the
> subscript of the variables change each time.
> THANK YOU!
-----------
  What kind of "sign pattern" are you looking for? Granted that each of the
matrices A2, A3, A4, A5, etc. you generate from a given P will be nilpotent if
A1 is, but I don't seen any repeating patterns of signs in them.

  However, to answer your question, you could always store your results in a
four-dimensional array as follows. Let nilpotent A and the number of
repetitions N be given.

P = randn(4,4,N);
M = zeros(4,4,4,N);
for k = 1:N
  p = P(:,:,k);
  for m = 1:4
   A = p*A*inv(p);
   M(:,:,m,k) = A;
  end
end

  Alternatively you could place each 4 x 4 matrix A in a 16 x 1 arrangement in
a three-dimensional 16 x 4 x N array.

P = randn(4,4,N);
M = zeros(16,4,N);
for k = 1:N
  p = P(:,:,k);
  for m = 1:4
   A = p*A*inv(p);
   M(:,m,k) = A(:);
  end
end

  Note that you should not do this for too large a value of N, because
cumulative round-off errors will gradually erode the condition of A being
nilpotent. That is, the size of elements in A^4 would gradually increase in
size due to accumulating round-off errors. Note also that by chance some of
the p matrices may be nearly singular which will no doubt make the round-
off error situation worse.

Roger Stafford