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 ?
They cover how inequalities behave, squares are never negative, the arithmetic-geometric mean inequality, the harmonic mean, symmetry in algebra, the rearrangement inequality, and the Cauchy-Schwarz inequality.
3)] for any couple vectors the Cauchy-Schwarz inequality is true that for the vectors (1) inequality gives an implication
Subsequently, we give a low bound on the mutual coherence of sensing matrix using the inverse formula of Cauchy-Schwarz inequality and then prove that it satisfies the RIP with suitable parameters.
Using the triangle inequality and Cauchy-Schwarz inequality, we have
By using the Cauchy-Schwarz inequality together with the use (2.
where the last inequality follows from the Cauchy-Schwarz inequality.
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
The second part follows immediately from the Cauchy-Schwarz inequality and from the well-known sum
where we used (25) in the first estimate, Cauchy-Schwarz inequality in the second and Claim 2 in the last one.
Indeed, applying the Cauchy-Schwarz inequality for the left hand of(2.