Re: Decompsition of a linear operator.


"leox" <leonid.uk@xxxxxxxxx> wrote in message
news:1149428975.592891.108590@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Let A be a nonsingular linear operator of a finite-dimensional vector
space. It is well know that A allows the decomposiotion A=HU where H is
a positive defined nonsingular operator and U is a unitary operator.
Suppose now that A be singular linear operator. Is there any
decomposition of A similar to the above decomposition?


check out

http://en.wikipedia.org/wiki/Singular_value_decomposition


You can easily write A as a sum of a nonsingular and singular matricies.
This could help in some problems.

I do believe there are several different decompositions of singular
matricies if I'm not mistaken.

Jon


.

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