Student Support Forum: 'Orthonormal hermitian matrices' topicStudent Support Forum > General > "Orthonormal hermitian matrices"

 Next Comment > Help | Reply To Topic
 Author Comment/Response Alex 02/28/07 04:31am Hi, I'm trying to generate an orthonormal basis of Hermitian traceless matrices. The inner product is Tr[AB]. I managed to generate the basis, but I can't get to orthonormalize it. The function GramSchmidt just doesn't evaluate. Here's the code << LinearAlgebra`Orthogonalization` Basis[d_] := ( b = {{IdentityMatrix[d]}}; (*t1 = Table[{i, i} -> 1, {i, 1, d}];*) t1 = {}; For[i = 1, i ≤ d, i++, For[j = i + 1, j ≤ d, j++, AppendTo[t1, {{i, j} -> 1, {j, i} -> 1}]; AppendTo[t1, {{i, j} -> \[ImaginaryI], {j, i} -> -\[ImaginaryI]}]; ]; ]; For[i = 1, i ≤ d - 1, i++, AppendTo[t1, {{i, i} -> 1, {d, d} -> -1}]; ]; AppendTo[b, SparseArray[#, {d, d}, 0] & /@ t1]; Flatten[b, 1] // Normal ) CM[v_, b_] := Sum[v〚i〛b〚i〛, {i, 1, Length[v]}] Orthogonalize[b_] := ( v = Table[Table[ KroneckerDelta[i, j], {j, 1, Length[b]}], {i, 1, Length[b]}]; GramSchmidt[v, InnerProduct -> (Tr[CM[#1, b].CM[#2, b]]) &] ) URL: ,

 Subject (listing for 'Orthonormal hermitian matrices') Author Date Posted Orthonormal hermitian matrices Alex 02/28/07 04:31am Re: Orthonormal hermitian matrices Forum Modera... 03/23/07 4:16pm
 Next Comment > Help | Reply To Topic