Question

अन्तर गुजन समाह में कोशी-स्वार्ज असमिका का कथन लिखिए एवं सिद्ध कीजिए।
State and prove Cauchy-Schwarz inequality in an inner product space
Sartinn-R​

Answer 1

Cauchy-Schwarz inequality in an inner product space:-

• An inner product practically enables one to use the tools typical of geometry in Rn in a more common context.
• Going with this validity then the following term in the explanation of γ is how one interprets the prediction of β onto α.
• The justification for looking at this is that presently the vectors β, the above projection, and their distinction form a "right triangle".
• Now Cauchy-Schwarz is the same as triangle inequality (broadening both sides in the triangle inequality), but by Pythagoras's Theorem, we can explicitly calculate the various standards implicated.

Proving Cauchy-Schwarz inequality in an inner product space

• The observable understanding of the Cauchy Schwarz inequality and its basic proof is that the vector v has deteriorated into a vector t perpendicular to w and the vector v − t.
• These three vectors set a right triangle.
• The Pythagorean theorem suggests the Cauchy Schwarz inequality since one outcome of the theorem is that in any right triangle the length of any leg is bound by the extent of the hypotenuse.

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