Editing Cauchy–Binet formula (section)

{{Short description|Identity in linear algebra}}
In [[mathematics]], specifically [[linear algebra]], the '''Cauchy–Binet formula''', named after [[Augustin-Louis Cauchy]] and [[Jacques Philippe Marie Binet]], is an [[Identity (mathematics)|identity]] for the [[determinant]] of the [[matrix multiplication|product]] of two rectangular [[matrix (mathematics)|matrices]] of transpose shapes (so that the product is well-defined and [[Square matrix|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]].