The Cauchy-Binet Formula is an identity in linear algebra, named after Augustin-Louis Cauchy and Jacques Philippe Marie Binet, for the determinant of the product of two rectangular matrices whose shapes are transposes of each other, so that the product is square and well defined. It generalizes the simpler fact that the determinant of a product of square matrices equals the product of their determinants, and it holds for matrices with entries drawn from any commutative ring.
Facts
StatementAn identity for the determinant of the product of two rectangular matrices of transpose shapes, so that the product is well-defined and square. 2 Classification
Statement Form Connections
Sources
1. Wikipedia: Cauchy-Binet formula
WikipediaLead section, statement-form referenceQuote, Lead section, statement-form reference
It generalizes the statement that the determinant of a product of square matrices is equal to the product of their determinants.
2. Cauchy-Binet formula (Wikipedia)
Intro, sentence 1Quote, Intro, sentence 1
an identity for the determinant of the product of two rectangular matrices of transpose shapes
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