 Binet–Cauchy identity

In algebra, the Binet–Cauchy identity, named after Jacques Philippe Marie Binet and Augustin-Louis Cauchy, states that

for every choice of real or complex numbers (or more generally, elements of a commutative ring).Setting "ai" = "ci" and "bj" = "dj", it gives the Lagrange's identity, which is a stronger version of the Cauchy–Schwarz inequality for the Euclidean space formula_2.