What is the maximum dimension of space $V$?

Asked Jul 16 '19 at 14:20

Active Jul 16 '19 at 14:32

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Problem

Let $M_{n}(\mathbb{R})$ is a vector space of square matrix with size $n \times n$. Assume $V$ is a subspace of $M_{n}(\mathbb{R})$ such, that all its elements have zero determinant. What is the maximum dimension of space $V$?

Question

Can somebody give me a hint on how to tackle the problem above? Thanks.

edited Jul 16 '19 at 14:32

David C. Ullrich

92,839

asked Jul 16 '19 at 14:20

Roman Dryndik

See https://math.stackexchange.com/questions/66877/max-dimension-of-a-subspace-of-singular-n-times-n-matrices – cmk Jul 16 '19 at 14:23
Thanks @cmk. Looks like my question duplicates the one from your link. – Roman Dryndik Jul 16 '19 at 14:24
No problem! $\ $ – cmk Jul 16 '19 at 14:30

What is the maximum dimension of space $V$?

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