> I could be misunderstanding, but I think you'd get all the algebraic
> content out of it by computing the dimensions of the image and kernel,
> then working with them from there on. Why would you want to have a
> matrix decomposition that separated them?
Well. Sometimes you want to know a solution to a problem and not only the dimension of the solution space : )
Also for composition: If you have "compatible" matrices B,C. How do you compute the restriction: A|_ker(B), A|_im(B) or co-restrictions (factor projections): A/ker(C), A/im(C), etc.
Well. Sometimes you want to know a solution to a problem and not only the dimension of the solution space : )
Also for composition: If you have "compatible" matrices B,C. How do you compute the restriction: A|_ker(B), A|_im(B) or co-restrictions (factor projections): A/ker(C), A/im(C), etc.