The generating identity of Cauchy-Schwarz-Bunyakovsky inequality (Q1025795)

This paper proposes an identity which gives rise to the Cauchy-Schwarz-Bunyakovsky inequality for the general case, based on the concept of the tensor product of vector spaces. First, a fundamental relationship is established between the inner product in a vector space \(V\) and a particular inner product in the tensor product of \(V\) with itself. Then, a Pythagorean relation, involving symmetric and antisymmetric parts of a tensor, is derived and manipulated to obtain the desired identity.