Tien-Cheng Huang

In algebra, Lagrange's identity, named after Joseph Louis Lagrange, is: which applies to any two sets {a1, a2, . . ., an} and {b1, b2, . . ., bn} 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–Cauchy identity. In a more compact vector notation, Lagrange's identity is expressed as: where a and b are n-dimensional vectors with components that are real numbers. The extension to complex numbers requires the interpretation of the dot product as an inner product or...