orthogonal basis of the vector space of nxn Hermitian matrices
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From: magya_bloom on 22 Jul 2010 12:03 anyone knows the above (that is relative to the trace(AB) where A and B are Hermitian)? thanks.
From: Maarten Bergvelt on 22 Jul 2010 16:57 On 2010-07-22, magya_bloom(a)yahoo.com <magya_bloom(a)yahoo.com> wrote: > anyone knows the above (that is relative to the trace(AB) where A and > B are Hermitian)? thanks. Why don't you choose your favorite basis of that space and do the Gram-Schmidt song-and-dance routine? -- Maarten Bergvelt
From: Gerry on 22 Jul 2010 18:21 On Jul 23, 6:57 am, Maarten Bergvelt <be...(a)math.uiuc.edu> wrote: > On 2010-07-22, magya_bl...(a)yahoo.com <magya_bl...(a)yahoo.com> wrote: > > > anyone knows the above (that is relative to the trace(AB) where A and > > B are Hermitian)? thanks. > > Why don't you choose your favorite basis of that space and do the > Gram-Schmidt song-and-dance routine? Maybe OP wants a formula that works for all n. -- GM
From: Stephen Montgomery-Smith on 22 Jul 2010 21:25 magya_bloom(a)yahoo.com wrote: > anyone knows the above (that is relative to the trace(AB) where A and > B are Hermitian)? thanks. Matrices which are diagonal with diagonal entries (0,0,...,0,1,0,...0), and matrices which for i not equal to j have the entries a_ij and a_ji equal to 1/sqrt(2) and all other entries zero.
From: Stephen Montgomery-Smith Montgomery-Smith on 23 Jul 2010 19:22
On Jul 22, 8:25 pm, Stephen Montgomery-Smith <step...(a)math.missouri.edu> wrote: > magya_bl...(a)yahoo.com wrote: > > anyone knows the above (that is relative to the trace(AB) where A and > > B are Hermitian)? thanks. > > Matrices which are diagonal with diagonal entries (0,0,...,0,1,0,...0), > and matrices which for i not equal to j have the entries a_ij and a_ji > equal to 1/sqrt(2) and all other entries zero. I forgot the matrices in which a_ij is i/sqrt(2) and a_ji is -i/ sqrt(2). |