linear algebra proof

Linear spaces and subspaces, linear transformations, bases, etc.

linear algebra proof

Postby davide940 on Fri Apr 18, 2014 1:06 pm

so that and is an invertible matrix. Proof that

by definition is invertible so:
so
Then if
Here I can only say if and not if and only if because the product can be 0 even though both matrices are not 0.
I would like to know if I had it all wrong.
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Postby stapel_eliz on Fri Apr 18, 2014 6:56 pm

davide940 wrote: so that and is an invertible matrix. Proof that

Please define your terms. What is "Mn(R)"? Is the "n" supposed to be subscripted? Does the "R" stand for "the set of real numbers"? What is "0n"? Is this perhaps an n-by-n zero matrix?

Thank you! :wink:
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