Let $A$ be a subspace of $M_{n\times n}(F)$, prove that if $\dim(A)> n^2-n$ , $\exists$ invertible matrix $M \in A$.

Asked Dec 04 '16 at 07:08

Active Dec 04 '16 at 07:40

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Let $A$ be a subspace of $M_{n\times n}(F)$, prove that if $\dim(A)> n^2-n$ , $\exists$ invertible matrix M $\in$ $A$.

edited Dec 04 '16 at 07:40

asked Dec 04 '16 at 07:08

Y. Hu

3

See http://math.stackexchange.com/questions/66877/max-dimension-of-a-subspace-of-singular-n-times-n-matrices – levap Dec 04 '16 at 08:57
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I posted an answer to the question of which it was marked as a duplicate: http://math.stackexchange.com/a/2045640/9911 – doetoe Dec 05 '16 at 23:13

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