Lagrange's identity [SEP] named after
Lagrange's identity
In algebra, Lagrange's identity, named after Joseph Louis Lagrange, is:
which applies to any two sets {"a", "a", . . ., "a"} and {"b", "b", . . ., "b"} of real or complex numbers (or more generally, elements of a commutative ring). This identity is a generalisation of the Brahmagupta–Fibonacci identity and a special form of the Binet
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 "a" = "c" and "b" = "d", it gives the Lagrange's identity, which is a stronger version of the Cauchy–Schwarz inequality for the Euclidean space formula_2.
The Binet–Cauchy