as follows : Prove that there is no matrix A (other than the 0 matrix) for which for every B.
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Originally Posted by adam63 Let as follows : Prove that there is no matrix A (other than the 0 matrix) for which for every B. let and suppose that is the standard basis for the vector space of all matrices over now for all if and only if for all but and thus therefore for all if and only if
Well, thank you very much! BTW, are you sure there is no other way, more 'elegant'?
Originally Posted by NonCommAlg let and suppose that is the standard basis for the vector space of all matrices over now for all if and only if for all but and thus therefore for all if and only if Originally Posted by adam63 Well, thank you very much! BTW, are you sure there is no other way, more 'elegant'? Now, I am not the most knowledgeable linear algebraist (? :S) in the world, but I now an "elegant" proof when I see one. That was an elegant proof.
Originally Posted by Drexel28 Now, I am not the most knowledgeable linear algebraist (? :S) in the world, but I now an "elegant" proof when I see one. That was an elegant proof. Thanks ! Just thought there would be something more 'verbal', or an assumption that would lead to a contradiction.
Originally Posted by adam63 Well, thank you very much! BTW, are you sure there is no other way, more 'elegant'? it's math, there's always another way! besides, looking for (possible) more elegant proofs is tempting when the problem is not straightforward.
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