Talk:Hermitian matrix

message: Hermitian matrices are defined much more generally. This article only deals with the most common case, complex numbers.  You just need  and a field and a fixed involutive automorphism and you can define hermitian matrix.  It is often done over finite fields, and it can also be define with other involutive automorphisms of the complex numbers than the usual conjugation.Evilbu 22:02, 4 February 2006 (UTC)
thread_title:  Initial Comments 

message: A* is the conjugate matrix of A.  Atranspose is the transposed matric of A.  The conjugate transpose is denoted A*transpose.  I  don't know off hand how to do the transpose symbol in Latex.  But it would look roughly like A*t.
: A* is the standard notation for conjugate transpose in matrix theory, but may well denote the conjugate matrix in other displines further removed from maths. See Talk:Conjugate matrix for some previous discussion. -- Jitse Niesen (talk) 04:24, 10 June 2006 (UTC)
thread_title:  Conjugate transpose 

message: I think AB=BA must not be true for hermitian matrix. For example think of a1:matrix([0,0,0,1],[0,0,1,0],[0,1,0,0],[1,0,0,0]) and a2:matrix([0,0,0,-%i],[0,0,%i,0],[0,-%i,0,0],[%i,0,0,0]). a1 * a2 = matrix([%i,0,0,0],[0,-%i,0,0],[0,0,%i,0],[0,0,0,-%i])!=matrix([-%i,0,0,0],[0,%i,0,0],[0,0,-%i,0],[0,0,0,%i])=a2 * a1.
Or am I wrong?? (the matrices i took above are the dirac matrices)
:All diagonal matrices are Hermitian and commute, so AB = BA holds for that family. I hope that answers your question. -- Jitse Niesen (talk) 16:49, 8 January 2007 (UTC)
replies: text: slight clarification: All diagonal matrices with real entries are Hermitian and commute. Mct mht 17:00, 8 January 2007 (UTC)
thread_title:  anti commutative matrices can't be hermitian?? 

message: I personally find intuitive explanations
very important when learning math.
I have written an article:
 "Visualizing Hermitian Matrix as An Ellipse with Dr. Geo" for my students
and wonder if it is appropriate to link
to it from here.  —Preceding unsigned comment added by Ckhung (talk • contribs) 02:11, August 28, 2007 (UTC) 
:That looks appropriate. I think your explanation is not succinct enough to include in an encyclopaedia but it does add to the article. So I added the link. Thanks. -- Jitse Niesen (talk) 03:44, 28 August 2007 (UTC)
replies: text: that works only for positive matrix though. maybe relocate the link to that article? one particular instance is the inertia ellipsoid from mechanics. Mct mht 04:59, 28 August 2007 (UTC)
thread_title:  some more intuitive explanations please? 

message: The last section on circles looks like a very specific use of Hermitian matrices, rather than general information. Perhaps it should be moved into an "Examples" section with a few other bullet points, or just outright deleted?  —Preceding unsigned comment added by Evanpw (talk • contribs) 22:37, 24 July 2008 (UTC)
thread_title:  Section on "Circles" 

message: I had to change the statement about the dimension of the vector space of real symmetric matrices from n^2 to n(n+1)/2.  Someone had to have miscounted, because any n^2 dimensional subspace of M_n(R) is, of course, all of M_n(R).  Also some claification was needed for some 10%-true statements like: "The eigenvectors of a Hermitian matrix are orthogonal".  I also considered the statement " moreover, eigenvectors with distinct eigenvalues are orthogonal" to be irrelevant, since this isn't a special property of Hermetian matrices and it doesn't seem to be used later.  The important information is that the geometric multiplicity of the eigenvalues matches the algebraic multiplicity.  I hope the switch from \sigma to \lambda isn't too bad, I did that to come in line with the Eigendecomposition article, and to avoid confusion with the singular value decomposition.Rschwieb (talk) 20:14, 3 February 2011 (UTC)
replies: text: Buzz, you have been told several times in-thread that this edit is not a good one. I have reverted your edits. Blennow (talk) 06:20, 3 July 2015 (UTC)
thread_title:  General Corrections