1. Its length can be estimated using the Cauchy-Schwarz inequality : 2. By the Cauchy-Schwarz inequality , the equation gives the estimate: 3. Since positive semidefinite hermitian sesquilinear forms satisfy the Cauchy Schwarz inequality , the subset 4. A firmly non-expansive mapping is always non-expansive, via the Cauchy Schwarz inequality . 5. It follows, essentially from the Cauchy Schwarz inequality , that f " is absolutely summable. 6. It is a corollary of the Cauchy Schwarz inequality that the correlation cannot exceed 1 in absolute value. 7. The Cauchy & ndash; Schwarz inequality is met with equality when the two vectors involved are collinear. 8. It is also known in the Russian mathematical literature as the " Cauchy Bunyakovsky Schwarz inequality ". 9. The special case " q " 2 } } gives a form of the Cauchy Schwarz inequality . 10. Proof of this inequality is by the Cauchy-Schwarz inequality , see Borg ( pp . 152 153 ).
