A multilinear algebra proof of the Cauchy-Binet formula and a multilinear version of ParsevalÊs identity

Abstract

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. © 2013 Elsevier Inc.