Products, coproducts and singular value decomposition

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dc.creatorFauser, Bertfried
dc.date2004-02-28
dc.date.accessioned2026-07-07T07:40:08Z
dc.date.available2026-07-07T07:40:08Z
dc.descriptionProducts and coproducts may be recognized as morphisms in a monoidal tensor category of vector spaces. To gain invariant data of these morphisms, we can use singular value decomposition which attaches singular values, ie generalized eigenvalues, to these maps. We show, for the case of Grassmann and Clifford products, that twist maps significantly alter these data reducing degeneracies. Since non group like coproducts give rise to non classical behavior of the algebra of functions, ie make them noncommutative, we hope to be able to learn more about such geometries. Remarkably the coproduct for positive singular values of eigenvectors in $A$ yields directly corresponding eigenvectors in A\otimes A.
dc.description17 pages, three eps-figures
dc.identifierhttps://arxiv.org/abs/math-ph/0403001
dc.identifierhttp://arxiv.org/abs/math-ph/0403001
dc.identifierInt. J. Theor. Phys. Vol 45, No 9, 2006: 1731-1755
dc.identifierdoi:10.1007/s10773-006-9111-6
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/121693
dc.subjectMathematical Physics
dc.subject15A18; 16W30; 15A66
dc.titleProducts, coproducts and singular value decomposition
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