Binet–Cauchy identity
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In algebra, the Binet–Cauchy identity, named after Jacques Philippe Marie Binet and Augustin-Louis Cauchy, states that[1]
for every choice of real or complex numbers (or more generally, elements of a commutative ring).
Setting ai = ci and bj = dj, it gives Lagrange's identity, which is a stronger version of the Cauchy–Schwarz inequality for the Euclidean space
. The Binet-Cauchy identity is a special case of the Cauchy–Binet formula for matrix determinants.