schwarz inequality sentence in Hindi
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- Its length can be estimated using the Cauchy-Schwarz inequality:
- By the Cauchy-Schwarz inequality, the equation gives the estimate:
- Since positive semidefinite hermitian sesquilinear forms satisfy the Cauchy Schwarz inequality, the subset
- A firmly non-expansive mapping is always non-expansive, via the Cauchy Schwarz inequality.
- It follows, essentially from the Cauchy Schwarz inequality, that f " is absolutely summable.
- It is a corollary of the Cauchy Schwarz inequality that the correlation cannot exceed 1 in absolute value.
- The Cauchy & ndash; Schwarz inequality is met with equality when the two vectors involved are collinear.
- It is also known in the Russian mathematical literature as the " Cauchy Bunyakovsky Schwarz inequality ".
- The special case " q " 2 } } gives a form of the Cauchy Schwarz inequality.
- Proof of this inequality is by the Cauchy-Schwarz inequality, see Borg ( pp . 152 153 ).
- It can also be shown by an application of the Cauchy-Schwarz inequality to the time dependent intensity correlation function
- The fact that the above sum converges for every " x " follows from the Cauchy-Schwarz inequality.
- This technique can be used in the same manner to prove the generalized AM GM inequality and Cauchy Schwarz inequality in Euclidean space.
- In order to relate the two vectors | f \ rangle and | g \ rangle, we use the Cauchy Schwarz inequality which is defined as
- :In view of the Cauchy-Schwarz inequality, we also note that \ langle \ cdot, \ cdot \ rangle is continuous from to.
- Hence by the Cauchy Schwarz inequality either \ phi = e ^ { i \ beta } \ psi or \ phi is orthogonal to \ psi.
- The Cauchy Schwarz inequality is used to prove that the inner product is a continuous function with respect to the topology induced by the inner product itself.
- It uses only the arc length formula, expression for the area of a plane region from Green's theorem, and the Cauchy Schwarz inequality.
- Applying the Cauchy Schwarz inequality for integrals and sums to the Hlawka Zaremba identity, we obtain an L ^ 2 version of the Koksma Hlawka inequality:
- This can be shown by an application of the Cauchy-Schwarz inequality to the definition of g ^ { ( 2 ) } ( 0 ).
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