Polarization Identity - Formula

Formula

The various forms given below are all related by the parallelogram law:

2\|\textbf{u}\|^2 + 2\|\textbf{v}\|^2 = \|\textbf{u}+\textbf{v}\|^2 + \|\textbf{u}-\textbf{v}\|^2.

The polarization identity can be generalized to various other contexts in abstract algebra, linear algebra, and functional analysis.

Read more about this topic:  Polarization Identity

Famous quotes containing the word formula:

    “For the myth is the foundation of life; it is the timeless schema, the pious formula into which life flows when it reproduces its traits out of the unconscious.”
    —Thomas Mann (1875–1955)

    “I cannot give you the formula for success, but I can give you the formula for failure—which is: Try to please everybody.”
    —Herbert B. Swope (1882–1958)

    “Given for one instant an intelligence which could comprehend all the forces by which nature is animated and the respective positions of the beings which compose it, if moreover this intelligence were vast enough to submit these data to analysis, it would embrace in the same formula both the movements of the largest bodies in the universe and those of the lightest atom; to it nothing would be uncertain, and the future as the past would be present to its eyes.”
    —Pierre Simon De Laplace (1749–1827)