Finding Jordan Canonical Form (V and J) of a big square matrix

While using [V J] = jordan(A); for a 33x33 matrix A, I am getting the following error.

Code:

if true
  % code
end
N = 33;
W = zeros(N,N);
for i=1:N 
  for j = 1:N
      if(i ~= j)
          if(round(rand - 0.1))
              W(i,j)  = round(5*rand);
          end
      end
  end
end
[V J] = jordan(W);

Command Window:

if true
  % code
end
Warning: Found roots of the minimal polynomial that cannot be determined
in terms of radicals. [linalg::jordanForm] 
Error using mupadmex
Error in MuPAD command: The operand is invalid. [_index]
Evaluating: symobj::jordan
Error in sym/mupadmexnout (line 879)
      out = mupadmex(fcn,args{:});
Error in sym/jordan (line 34)
      [Vsym,Jsym] = mupadmexnout('symobj::jordan',A,'All');
Error in jordan (line 25)
 [V,J] = jordan(sym(A));

When I increase the size of the matrix A, I get the following error

if true
  % code
end
Error using mupadmex
Error in MuPAD command: Similarity matrix too large.
Error in sym/mupadmexnout (line 879)
      out = mupadmex(fcn,args{:});
Error in sym/jordan (line 34)
      [Vsym,Jsym] = mupadmexnout('symobj::jordan',A,'All');
Error in jordan (line 25)
 [V,J] = jordan(sym(A));

How can I get the jordan decomposition of bigger matrices say a maximum of 200x200 matrix??

[Rahul Singh]

Please help!

Answer 1

[Mukul Rao]

The Jordan function has an imposed size limit to help prevent exceedingly long calculations. In order to get around the error, execute this function instead:

>> feval(symengine, 'linalg::jordanForm', A, 'All')

Where "A" is the matrix which you are analyzing. Note that while this will bypass the size limitation, the calculation can take a very long time. If you are just interested in the eigenvalues and eigenvectors of the matrix, consider using the "eig" function instead.

[Rahul Singh]

It still fails.

Warning: Found roots of the minimal polynomial that cannot be determined in terms of radicals. [linalg::jordanForm]

[Mukul Rao]

Rahul, what release of MATLAB are you working with?

[Rahul Singh]

2013b, does it matter?