CBS inequality

Cauchy-Bunyakovski-Schwarz, [Cauchy-Schwarz inequality]?, [Schwarz inequality]?, and [Bunyakowski inequality]? all mean the same thing. Common to linear algebra, as true of vectors, and [real analysis]?, as true of both series and integration.

A concrete example: Euclidean Geometry in the plane (R^2). Here, the CBS inequality says that the area of a parallelogram is less than or equal to the product of the length of its sides. If the parallelogram happens to be a square, they are equal.

In the language of inner products, the CBS inequality says that <x, y>^2 <= <x, x> * <y, y>. An inner product really represents translating the Euclidean ideas of "area" and "angle" to more abstract spaces.