Home > Higher Algebra, Linear Algebra > Max Dimension for a linear space of singular matrices

Max Dimension for a linear space of singular matrices


Denote by V a vector space of singular (\det =0) n \times n matrices. What is the maximal dimension of such a space.

Denote by W a vector space of n \times n matrices with rank smaller or equal to p < n. What is the maximal dimension of such a space?

Answers: For the first question n^2-n and for the second question np. I will present proofs soon. The first problem is an obvious subcase of the second problem. For a nice proof, look at the answer given in the next link: http://math.stackexchange.com/questions/66877/max-dimension-of-a-subspace-of-singular-n-times-n-matrices

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