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:
“Having an identity at work separate from an identity at home means that the work role can help absorb some of the emotional shock of domestic distress. Even a mediocre performance at the office can help a person repair self-esteem damaged in domestic battles.”
—Faye J. Crosby (20th century)