Let A and B be real invertible n x n matrices so that B = (A(adsbygoogle = window.adsbygoogle || []).push({}); ^{T})^{-1}.

Show that B_{m}= (I - B_{1}A_{1}^{T})(A_{m}^{T})^{+}, where

B_{1}= [b_{1}, ...,b_{m}],

B_{m}= [b_{m+1}, ...,b_{n}],

A_{1}= [a_{1}, ...,a_{m}],

A_{m}= [a_{m+1}, ...,a_{n}].

Any pointers on how one would go about proving the above? I'm fresh out of ideas.

I'm not sure if the above statement is even actually true. Using random matrices in matlab, I have not found any counterexamples, though.

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# Homework Help: A short one on matrix multiplication

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