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Saturday, 22 September 2007

linear algebra - problems of subspace of M_n(C)

let Mn(c) denote the n times n matrices over the complex number field. N be a subspace of



Mn(C).



1 If there is no unitary lies in N, what is the maximum of the dimension of N can be?



It's easy to see that it is not less than n(n-1), I guess it's also tight, but I don't know if I am correct.



2 If all the rank of M lies in N are greater than a fixed integer k, what is the maximum of the dimension of N can be?

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