2
$\begingroup$

I am trying to get better at factoring matrices into special forms, e.g. block upper/lower triangular, so I was wondering whether I have this correct.

If matrices A through H are square and of the same size, nxn, is my matrix on the RHS correct? I basically treated the blocks as scalars, and performed the ordinary matrix multiplication techniques.

If it is correct, now what if A were mxn? Does this just require a bit more, e.g., so long as E and F are $nxm$, for the matrix multiplication to make sense, then again I can treat the blocks as scalars and proceed with ordinary matrix multiplication? (And if B were mxn, then G and H would need to be nxm, etc.)

$$ \begin{bmatrix} A & B \\ C & D \\ \end{bmatrix} * \begin{bmatrix} E & F \\ G & H \\ \end{bmatrix} = \begin{bmatrix} AE+BG & AF+BH \\ CE+DG & CF+DH \\ \end{bmatrix} $$

Thanks,

|cite|improve this question
$\endgroup$
1
$\begingroup$

Yes. But you should really try to convince yourself that it works, even for rectangular blocks (of proper sizes, of course).

|cite|improve this answer
$\endgroup$
  • $\begingroup$ Ok, got it -- thanks so much for the quick response, @MartinArgerami. Have a great day :-) $\endgroup$ – User001 Oct 1 '15 at 21:58

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.