Products, Coproducts, and Singular Value Decomposition

Author: Fauser, Bertfried¹

Source: International Journal of Theoretical Physics, Volume 45, Number 9, September 2006 , pp. 1718-1742(25)

Publisher: Springer

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Abstract:

Products 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, i.e. generalized eigenvalues, to these maps. We show, for the case of Grassmannand 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, makeing them noncommutative, we hope to be able to learn more about such geometries. A remarkabe thechnicallity is that the coproduct for positive singular values of eigenvectors in A yields directly corresponding eigenvectors in A⊗ A.

Keywords: products; coproducts; singular value decomposition; noncommutative function algebras

Document Type: Research article

DOI: 10.1007/s10773-006-9111-6

Affiliations: 1: Email: Bertfried.Fauser@uni-konstanz.de

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