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Topic: Symbolic Jordan Decomposition
Replies: 8   Last Post: Jan 12, 2012 10:30 AM

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Leslaw Bieniasz

Posts: 171
Registered: 12/13/04
Symbolic Jordan Decomposition
Posted: Jan 10, 2012 5:31 AM
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Hi,

I am not sure if you understand properly mu questions.
I am not asking what the Jordan Decomposition is; this is
a well known issue described in books. I may not be expert in this area,
but I know more or less what it is. I am also not asking how
to obtain the Jordan normal matrix form by using a pen and paper.
This task may indeed be the most convenient to accomplish by first solving
the characteristic equation, and then finding generalised eigenvectors,
etc.

I am asking how to devise a computer algorithm that can solve the task
symbolically (by which I mean playing with symbols, not concrete numbers,
even not exact numbers such as rational numbers).
There is a question how to represent the symbols and operations on them
in a computer, and what should be the operations to arrive at the Jordan
normal form in the simplest possible way, in cases when such a symbolic
solution is feasible (it will not be feasible, if closed form expresisons
for the eignvalues don't exist).

Leslaw




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