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Topic: Antihermitian

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	Properties of the D and D operators
		operators are unitary, they are hermitian or antihermitian depending on whether they are involutive or antiinvolutive, respectively.
		Antilinear operators do not give good quantum numbers, and their role is very different, depending on whether they are hermitian or antihermitian, Tables 1 and 2.
		This is in contrast to properties of linear operators, for which a linear combination of eigenstates, corresponding to the same eigenvalue, with arbitrary coefficients, is also an eigenstate with the same eigenvalue.
	www.fuw.edu.pl /~dobaczew/symhfx57w/node7.html (347 words)

	IngentaConnect AntiHermitian operators in atomic shell theory (Site not responding. Last check: 2007-10-29)
		AntiHermitian operators that are scalar with respect to the total angular momentum J and that act simultaneously on n electrons of the shell are shown to possess quasispin ranks K of opposite parity to n provided two conditions are satisfied.
		Examples of such operators for the f shell are four three-electron operators scalar with respect to S and L, and eight two-electron operators whose simultaneous spin and orbital ranks are 1 or 2.
		This property is examined by parallel methods for the antiHermitian and Hermitian forms, and several unexpected proportionalities are thereby explained.
	api.ingentaconnect.com /content/iop/jphysb/1997/00000030/00000004/art00004 (263 words)

	Re: Lie groups for grunts
		U(n) is the Lie group of complex unitary matrices of dimension n, and u(n) is its Lie algebra of complex antiHermitian matrices of dimension n.
		SU(n) is the Lie group of special complex unitary matrices of dimension n, and su(n) is its Lie algebra of traceless complex antiHermitian matrices of dimension n.
		Sp(n) is the Lie group of quaternionic unitary matrices of dimension n, and sp(n) is its Lie algebra of quaternionic antiHermitian matrices of dimension n.
	www.lns.cornell.edu /spr/2000-11/msg0029535.html (869 words)

	[No title]
		The eigenvectors of $A$ are often referred to as the \emph{normal modes} and the corresponding complex eigenvalues determine the growth/decay and oscillatory frequency of these modes.
		Now as is well known (and can be shown intuitively by discretization) the partial differential operators $\frac{\partial}{\partial x}$ and $\frac{\partial}{\partial y}$ are antihermitian and so it follows easily that the operator $A$ for the shallow water equations is also.
		This is commonly referred to as barotropic instability and occurs frequently in many situations in both atmosphere and ocean.
	www.math.nyu.edu /faculty/kleeman/Lecture3.tex (1645 words)

	Computing with Maple
		One of several VRML browsers available as a web-browser plug-in is Cosmo Player, which is available for several platforms free of charge from www.cosmosoftware.com.
		Page 171: The code to generate random hermitian and antihermitian matrices actually generates special cases with zeros on the leading diagonal.
		General random hermitian and antihermitian matrices can be generated by using more appropriate complex random number generators tailored to each case.
	centaur.maths.qmw.ac.uk /CwM (765 words)

	Special unitary group - Bvio (Site not responding. Last check: 2007-10-29)
		The Lie algebra corresponding to SU(n) is denoted by su(n).
		It consists of the traceless antihermitian n×n complex matrices, with the regular commutator as Lie bracket.
		Note that this is a real and not a complex Lie algebra.
	bvio.ngic.re.kr /Bvio/index.php/Special_unitary_group (327 words)

	[No title] (Site not responding. Last check: 2007-10-29)
		It is therefore possible to choose $\gamma^0$ to be hermitian.
		Similarly, we can choose the $\gamma^i$ to be antihermitian: $(\gamma^i)^\dag=-\gamma^i$ (since $(\gamma^i)^2$ has all non-positive eigenvalues, so $\gamma^i$ has all imaginary eigenvalues).\\ (Note that the representation we gave earlier has these hermiticity properties.)\\ It is easily checked that \begin{displaymath} \gamma^0\gamma^\mu(\gamma^0)^{-1}=(\gamma^\mu)^\dag \end{displaymath} for $m=0,1,2,3$.
		The vector space of possible $X$ forms the Lie algebra of $G$.\\ Examples: \begin{itemize} \item[1)]For $G=U(n)$, the Lie algebra $\rm{Lie}(U(n))$ is the set of antihermitian $n\times n$ matrices: $g\in U(n)$ close to $\mathbf{1}$ can be written $g=\mathbf{1}+\epsilon X$.
	people.pwf.cam.ac.uk /tw279/qft.tex (6902 words)

	CHROMA: taproj.cc Source File (Site not responding. Last check: 2007-10-29)
		\file 00005 * \brief Take the traceless antihermitian projection of a color matrix 00006 */ 00007 00008 #include "chromabase.h" 00009 #include "util/gauge/taproj.h" 00010 00011 namespace Chroma { 00012 00013 //!
		Take the traceless antihermitian projection of a color matrix 00014 /*!
		Generated on Sat Nov 19 03:06:16 2005 for CHROMA by
	www.jlab.org /~edwards/qcdapi/docs/level3/chroma/doxygen/taproj_8cc-source.html (67 words)

	Publications in physics and mathematics by Walter Pfeifer (Site not responding. Last check: 2007-10-29)
		Therefore, the text on hand can make the lead-in to this field easier.
		First, Lie algebras are defined and the su(N) algebras are introduced starting from antihermitian matrices.
		In chapter 3, the su(2) algebras, their multiplets and the direct product of the multiplets are investigated.
	www.walterpfeifer.ch (518 words)

	ipedia.com: Special unitary group Article (Site not responding. Last check: 2007-10-29)
		The corresponding Lie algebra is denoted by su(n).
		su(n) is spanned by the traceless antihermitian nxn compex matrices.
		For example, the following matrices form a basis for su(2) over R:
	www.ipedia.com /special_unitary_group.html (275 words)

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