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:

    “But suppose, asks the student of the professor, we follow all your structural rules for writing, what about that “something else” that brings the book alive? What is the formula for that? The formula for that is not included in the curriculum.”
    —Fannie Hurst (1889–1968)

    ““It’s hard enough to adjust [to the lack of control] in the beginning,” says a corporate vice president and single mother. “But then you realize that everything keeps changing, so you never regain control. I was just learning to take care of the belly-button stump, when it fell off. I had just learned to make formula really efficiently, when Sarah stopped using it.””
    —Anne C. Weisberg (20th century)

    “Beauty, like all other qualities presented to human experience, is relative; and the definition of it becomes unmeaning and useless in proportion to its abstractness. To define beauty not in the most abstract, but in the most concrete terms possible, not to find a universal formula for it, but the formula which expresses most adequately this or that special manifestation of it, is the aim of the true student of aesthetics.”
    —Walter Pater (1839–1894)