Cauchy-Schwarz inequality

Cauchy-Schwarz inequality

[kō·shē ′shwȯrts in·i′kwäl·əd·ē]
(mathematics)
The square of the inner product of two vectors does not exceed the product of the squares of their norms. Also known as Buniakowski's inequality; Schwarz' inequality.
References in periodicals archive ?
6) holds, by using the Cauchy-Schwarz inequality and dividing both sides of (3.
Recall the Cauchy-Schwarz inequality, which will be central to our proof, is
Notice that, in that case, the left-hand side of the Cauchy-Schwarz inequality can be written as the sum of all the entries in the matrix P, [<W, N'>.
The second part follows immediately from the Cauchy-Schwarz inequality and from the well-known sum
and this majorant is independent of [epsilon], and is absolutely convergent by (21) and the Cauchy-Schwarz inequality.
Indeed, applying the Cauchy-Schwarz inequality for the left hand of(2.
i] and applying the Cauchy-Schwarz inequality yields to
i]) above and the Cauchy-Schwarz inequality, we can easily derive the following estimates (cf.
h] (*,*) as well as the Cauchy-Schwarz inequality we get
which together with the Cauchy-Schwarz inequality implies that