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

• 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.

Ämnesord

NATURVETENSKAP  -- Matematik -- Algebra och logik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Algebra and Logic (hsv//eng)

Nyckelord

Cauchy-Binet theorem

Determinant

Matrix identities

Hilbert space

Parseval's identity

Multilinear algebra

Exterior products

Projections Pythagorean theorem

Fock space

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