[ ] Let be any matrices with entries from and Let and denote the trace of and the identity matrix respectively.

Find some such that

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- Aug 15th 2010, 10:44 AMNonCommAlgCommuting Matrices
[ ] Let be any matrices with entries from and Let and denote the trace of and the identity matrix respectively.

Find some such that - Aug 16th 2010, 06:29 AMNonCommAlg
i don't have to mention that i'm not interested in a direct solution. anyway, here is a hint for those who like the problem:

__Spoiler__:

by the way, the result can be extended to commuting matrices but the solution to this general case is much harder. - Aug 20th 2010, 12:49 AMhalbardCommuting(?) matrices
This is a particular consequence of a very well-known result. For any matrices and

In particular, if then

__Spoiler__:

Incidentally, holds for all matrices and . What is ? - Aug 20th 2010, 07:15 AMNonCommAlg