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.

Finally, using the

Cauchy-Schwarz inequality, we obtain

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.