Re: Maximal dimension of vector space

Mate <mmatica@xxxxxxxxxxx> writes:

For n a positive integer, let V be a real vector space containing n x
n real matrices
such that trace(A B) = 0 for each A,B in V.
What is the maximal dimension for such a V?

You can certainly get (n-1)(n-2)/2, taking all strictly upper triangular
matrices. I don't see how you could do better with real matrices, though
you could with complex matrices.
--
Robert Israel israel@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada
.

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