User abcba - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-21T13:38:12Z http://mathoverflow.net/feeds/user/4965 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/19591/dimension-of-subalgebras-of-a-matrix-algebra Dimension of subalgebras of a matrix algebra abcba 2010-03-28T05:46:51Z 2011-07-06T23:04:39Z <p>If n is given and A is a subalgebra of M_n(C), the algebra of n-by-n matrices with entries in the field of complex numbers, then what are the possible values of dimension of A as a vector space over C?</p> http://mathoverflow.net/questions/19591/dimension-of-subalgebras-of-a-matrix-algebra Comment by abcba abcba 2010-03-28T08:02:31Z 2010-03-28T08:02:31Z Ok, I just found out that there is an interesting result due to Schur which gives a partial answer to my question. Here it is for those who are interested: If F is a field, then there exists a &quot;commutative&quot; subalgebra A of M_n(F) with dim_F A = k if and only if k \leq [n^2/4] + 1, where [ ] is the floor function. I'm starting to think that there exists a subalgebra of M_n(F) of any dimension!