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 denote the norm of vector x and the inner product of vectors x and y. Then the underlying theorem, attributed to Fréchet, von Neumann and Jordan, is stated as:

In a normed space (V, ), if the parallelogram law holds, then there is an inner product on V such that for all .

Read more about Polarization Identity:  Formula

Famous quotes containing the word identity:

    For the mother who has opted to stay home, the question remains: Having perfected her role as a caretaker, can she abdicate control to less practiced individuals? Having put all her identity eggs in one basket, can she hand over the basket freely? Having put aside her own ambitions, can she resist imposing them on her children? And having set one example, can she teach another?
    Melinda M. Marshall (20th century)