Cauchy–Binet Formula

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What is Cauchy–Binet formula?

In mathematics, specifically linear algebra, the Cauchy–Binet formula, named after Augustin-Louis Cauchy and Jacques Philippe Marie Binet, is an identity for the determinant of the product of two rectangular matrices of transpose shapes (so that the product is well-defined and square). It generalizes the statement that the determinant of a product of square matrices is equal to the product of their determinants. The formula is valid for matrices with the entries from any commutative ring.

Technology Types

arrangementarrayaugustin-louis cauchycognitive factordeterminantmathematical theoremmatricematrixpropositionstatementtheoremtheory

Synonyms

Binet-Cauchy formulaCauchy Binet formulaCauchy-Binet formula

Translations

Fórmula de Binet-Cauchy (pt)Formula di Cauchy-Binet (it)Satz von Binet-Cauchy (de)Формула Бине — Коши (ru)Формула Біне — Коші (uk)صيغة كوشي-بينيه (ar)코시-비네 공식 (ko)コーシー・ビネの公式 (ja)柯西–比内公式 (zh)

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