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Topic: Antilinear

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	Properties of the D and D operators
		Properties of these operators are very different depending on whether they are linear or antilinear.
		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.
	info.fuw.edu.pl /~dobaczew/symhfx57w/node7.html (347 words)

	Hermitian Conjugation
		Thus the transpose of an antilinear map whose outputs are linear will be a linear map whose outputs are antilinear.
		Now, for any linear or antilinear f, f+T(f) is manifestly symmetric; while f-T(f) is manifestly antisymmetric; and the average of these two is f.
		However, an antilinear (dual(V): g V) can; g(i.u,i.u) = (i).g(u,i.u) = (i).i.g(u,u) and (*i).i is given to be positive (given that i is non-zero); indeed, the same holds true for any non-zero scalar in place of i.
	www.chaos.org.uk /~eddy/math/linear/Hermite.html (2542 words)

	Physics Help and Math Help - Physics Forums - View Single Post - Time reversibility Schrodinger Eq.
		T is an antilinear operator (I'll explain later why).
		T is an antilinear operator due to the representation of the time reversal (t into —t) symmetry in the Hilbert space of QM (Wigner’s theorem).
		The definition of T as an antilinear operator comes from the structure of the space time (projective representation of a discrete symmetry group).
	www.physicsforums.com /showpost.php?p=353327&postcount=9 (918 words)

	Unitary Transformations
		I shall not, for the present at least, assume that g is positive definite; I shall mainly focus on the case where it is symmetric and invertible.
		Since a composite of two antilinears is linear, rather than antilinear, and I want to compose unitary mappings, the linear g-unitary mappings present themselves as the more convenient of the pair of isomorphic notions.
		is a linear unitary; indeed, any composite of unitaries will be unitary, and either linear or antilinear according as an even or odd number of the unitaries composed were antilinear.
	www.chaos.org.uk /~eddy/math/linear/unitary.html (2031 words)

	[No title]
		is one of the antilinear elements of D
		After Wigner, the term corepresentation is used here because the representations of groups containing antilinear operators are not representations in the usual sense.
		(108) implies that the homomorphism between the group multiplication and the multiplication of representation matrices no longer holds when the group contains antilinear operators.
	info.fuw.edu.pl /~dobaczew/symhfx57w/node13.html (402 words)

	CiteULike: Constructing N-qubit entanglement monotones from anti-linear operators (Site not responding. Last check: 2007-10-23)
		We present a method to construct entanglement measures for pure states of multipartite qubit systems.
		The key element of our approach is an antilinear operator that we call comb in reference to the hairy-ball theorem.
		We give alternative formulae for the concurrence and the 3-tangle as expectation values of certain antilinear operators.
	www.citeulike.org /user/yinzhangqi/article/134453 (150 words)

	AMCA: Intrinsic centrality and associated classifying properties by Dominique Bourn
		A first aspect of the discriminatory power of this additive core is given by the following table, where \Omega(C) is the ideal of null maps, and where the intersection of the line L and the column D defines the class of categories which satisfies the property L = D :
		The paradigmatic examples of respectively linear, additive, antilinear and antiadditive categories are CoM, Ab, the category PreH of preHeyting algebras, the category IMag of idempotent unitary magmas.
		The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Mathematical Conference Abstracts.
	at.yorku.ca /c/a/j/f/46.htm (575 words)

	Atlas software user guide -- Real forms (Site not responding. Last check: 2007-10-23)
		Let G be a connected complex reductive algebraic group.
		According to general principles in algebraic geometry, a real form of G is an antilinear involution of G; the set of fixed points of the involution is denoted G(R) and is a real reductive group, often non-connected.
		Therefore, in this program we always represent real forms through ordinary involutions of G. To relate our data to perhaps more familiar objects, one should think of our involution θ as the complexification of a Cartan involution for G(R).
	atlas.math.umd.edu /software/doc/realforms.html (189 words)

	Test functions
		Here we use the Riesz representation theorem and duality for Hilbert spaces.
		The map use here is supposed to be linear not antilinear, i.e.,
		So the idea is to make the space of `test functions' as small as reasonably possible, while still retaining density in reasonable spaces.
	www-math.mit.edu /~rbm/18.155-F02/Lecture-notes/node7.html (517 words)

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