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.
Konstantopoulos, T. (2013). A multilinear algebra proof of the Cauchy-Binet formula and a multilinear version of ParsevalÊs identity. Linear Algebra and Its Applications, 439(9), 2651–2658. https://doi.org/10.1016/j.laa.2013.07.009