#Cauchy shwartz inequality proof

11 messages · Page 1 of 1 (latest)

north sail
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Can someone explain how to prove (I am in precalc)?

Proofs in my class mean changing only one side to make it equal to the other

Would be much appreciated if you could write it out and explain the steps thank you

molten sigilBOT
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gilded bone
# north sail Can someone explain how to prove (I am in precalc)? Proofs in my class mean cha...

https://en.wikipedia.org/wiki/Cauchy–Schwarz_inequality

Cauchy–Schwarz inequality

The Cauchy–Schwarz inequality (also called Cauchy–Bunyakovsky–Schwarz inequality) is an upper bound on the inner product between two vectors in an inner product space in terms of the product of the vector norms. It is considered one of the most important and widely used inequalities in mathematics.
Inner products of vectors can describe finite s...

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Multiple ways to go about this.

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The most common is knowing that $|\langle \textbf{u, v}\rangle|\le ||\textbf{u}||||\textbf{v}||$, where $\textbf{u}$ and $\textbf{v}$ are vectors.

upper coveBOT
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Kocher

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gilded bone
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You can also just consider a quadratic and it's discriminant.

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Specifically this.

image.png
timber hingeBOT
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@north sail

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honest timber
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U could also consider it as a special case of Holders inequality. Where p=q=2.