simplification in matrices



-----maxima-bounces at math.utexas.edu wrote: -----


>thank you very much for your valuable help. It would be very useful for me
>if Maxima had a vector object. Functions like finding the vector
associated
>to a skew-symmetric matrix are very useful in vector calculus. Also things
>like decomposing a symmetric or skew-symmetric matrix in terms of its
>invariants would be helpful.

Maybe you don't need a vector to do want you need to do. Here are some
examples:

Define m to be an antisymmetric matrix

  (%i41) m : matrix([0,1,1],[-1,0,1],[-1,-1,0])$

Make a list of the traces of m, m^2, and m^3

  (%i42) makelist(mat_trace(m^^k),k,1,3);
  (%o42) [0,-6,0]

Express m as a linear combination of projection matrices

  (%i43) spectral_rep(m);
  (%o43) --- long expression deleted----

Verify the spectral representation

  (%i44) expand(m - first(%) . second(%));
  (%o44) matrix([0,0,0],[0,0,0],[0,0,0])

Compute exp(%i * m * t)

  (%i47) matrixexp(m, %i*t);
  (%o47) -- long expression deleted----

Maybe these examples will get you started. Or if there is something else,
maybe we all could help you figure out how to that too.

Barton