A multilinear algebra proof of the Cauchy-Binet formula and a multilinear version of Parseval%26apos;s identity

作者：Konstantopoulos Takis^*

来源：Linear Algebra and Its Applications, 2013, 439(9): 2651-2658.

DOI：10.1016/j.laa.2013.07.009

• Cauchy-Binet theorem
• Determinant
• Matrix identities
• Hilbert space
• Parseval%26apos
• s identity
• Multilinear algebra
• Exterior products
• Projections Pythagorean theorem
• Fock space

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.

• 出版日期2013-11-1