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A multilinear algebra proof of the Cauchy-Binet formula and a multilinear version of Parseval's identity
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
2013 (English)In: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 439, no 9, 2651-2658 p.Article in journal (Refereed) Published
Abstract [en]

We prove the Cauchy-Binet determinantal formula using multilinear algebra by first generalizing it to an identity not involving determinants. By extending the formula to abstract Hilbert spaces we obtain, as a corollary, a generalization of the classical Parseval identity.

Place, publisher, year, edition, pages
2013. Vol. 439, no 9, 2651-2658 p.
Keyword [en]
Cauchy-Binet theorem, Determinant, Matrix identities, Hilbert space, Parseval's identity, Multilinear algebra, Exterior products, Projections Pythagorean theorem, Fock space
National Category
Algebra and Logic
Identifiers
URN: urn:nbn:se:uu:diva-306394DOI: 10.1016/j.laa.2013.07.009ISI: 000324966800011OAI: oai:DiVA.org:uu-306394DiVA: diva2:1044392
Available from: 2016-11-03 Created: 2016-10-27 Last updated: 2016-11-03Bibliographically approved

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