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