A multilinear algebra proof of the Cauchy-Binet formula and a multilinear version of Parseval's identity

DOI10.1016/j.laa.2013.07.009zbMath1283.15028arXiv1305.0644OpenAlexW2963601688MaRDI QIDQ2435424

Takis Konstantopoulos

Publication date: 19 February 2014

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1305.0644

zbMATH Keywords

projectionsHilbert spacedeterminantFock spacemultilinear algebraexterior productsPythagorean theoremmatrix identitiesParseval's identityCauchy-Binet theorem

Mathematics Subject Classification ID

Determinants, permanents, traces, other special matrix functions (15A15) Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) (46C05) Matrix equations and identities (15A24) Multilinear algebra, tensor calculus (15A69)

Related Items (1)

Cauchy-Binet for pseudo-determinants

Cites Work

• A combinatorial approach to matrix algebra
• Apolarity and canonical forms for homogeneous polynomials
• A bijective proof of Muir's identity and the Cauchy-Binet formula
• Noncommutative determinants, Cauchy-Binet formulae, and Capelli-type identities. I: Generalizations of the Capelli and Turnbull identities
• An Introduction to Random Matrices
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