Polarization identity

In mathematics, the polarization identity is any one of a family of formulas that express the inner product of two vectors in terms of the norm of a normed vector space. Let ‖ x ‖ {displaystyle |x|} denote the norm of vector x and ⟨ x ,   y ⟩ {displaystyle langle x, y angle } the inner product of vectors x and y. Then the underlying theorem, attributed to Fréchet, von Neumann and Jordan, is stated as: In mathematics, the polarization identity is any one of a family of formulas that express the inner product of two vectors in terms of the norm of a normed vector space. Let ‖ x ‖ {displaystyle |x|} denote the norm of vector x and ⟨ x ,   y ⟩ {displaystyle langle x, y angle } the inner product of vectors x and y. Then the underlying theorem, attributed to Fréchet, von Neumann and Jordan, is stated as: