List questions from cauchy-schwarz-inequality

Published on 30 Mar 2020 - 2:38

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Proving $\def\n#1{\left(\frac12+\sum\limits_{k=1}^n{#1}^{k^2}\right)}\n{a}\n{b}\ge{\n{(ab)}}^2$

Published on 04 Apr 2020 - 0:50

80

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Explanation for Bound of Cauchy Inequality

Published on 04 Apr 2020 - 13:08

50

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Is $|\langle Ax, y\rangle|^4 \leq \langle |A|^{2}x, x\rangle\langle |A^*|^{2}y, y\rangle$?

Published on 05 Apr 2020 - 5:29

1.2k

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Bound for expectation of product of dependent random variables

Published on 05 Apr 2020 - 19:37

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how to prove this inequality $(x-1)^2+(y-1)^2+(z-1)^2+(u-1)^2+(w-1)^2+(2v+1)^2\ge 4$

Published on 07 Apr 2020 - 6:44

135

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Understanding an application of the Cauchy–Schwarz inequality

Published on 08 Apr 2020 - 5:35

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A squared integrals

Published on 28 Mar 2026 - 10:36

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Proving $ \mid a - x| > |b - x|$ implies $(a - b)\cdot(x-b)<0$ where $a,b,x\in\mathbb{R}^N$

Published on 23 Feb 2026 - 1:07

144

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Proving $\sum\limits_{\rm cyc} 1/(a^2 -b+4) \geq3/4$

Published on 25 Mar 2026 - 9:37

73

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Finiteness of expectation of product

Published on 27 Mar 2026 - 5:49

452

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Pearson’s Correlation Coefficient >=-1 & <=1

Published on 28 Mar 2026 - 4:52

396

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If $x,y,z \in \mathbb{R}$, $x^2+4y^2+16z^2=48, xy+4yz+2zx=24$, then find $x^2+y^2+z^2$.

Published on 12 Apr 2020 - 15:41

101

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Framing problem : Show that $\frac{x^2}{yz+1}+\frac{y^2}{zx+1}+\frac{z^2}{xy+1}\leq\frac{x^2+y^2+z^2}{4} +1$

Published on 13 Apr 2020 - 19:12

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If $a,b,c$ are the sides of a triangle, then $\dfrac{a}{b+c-a}+\dfrac{b}{c+a-b}+\dfrac{c}{a+b-c}$ is:

Published on 25 Mar 2026 - 12:41

List Question

$\langle Ax,x \rangle^4\leq \langle A^4x,x\rangle$

Proving $\def\n#1{\left(\frac12+\sum\limits_{k=1}^n{#1}^{k^2}\right)}\n{a}\n{b}\ge{\n{(ab)}}^2$

Explanation for Bound of Cauchy Inequality

Is $|\langle Ax, y\rangle|^4 \leq \langle |A|^{2}x, x\rangle\langle |A^*|^{2}y, y\rangle$?

Bound for expectation of product of dependent random variables

how to prove this inequality $(x-1)^2+(y-1)^2+(z-1)^2+(u-1)^2+(w-1)^2+(2v+1)^2\ge 4$

Understanding an application of the Cauchy–Schwarz inequality

A squared integrals

Proving $ \mid a - x| > |b - x|$ implies $(a - b)\cdot(x-b)<0$ where $a,b,x\in\mathbb{R}^N$

Proving $\sum\limits_{\rm cyc} 1/(a^2 -b+4) \geq3/4$

Finiteness of expectation of product

Pearson’s Correlation Coefficient >=-1 & <=1

If $x,y,z \in \mathbb{R}$, $x^2+4y^2+16z^2=48, xy+4yz+2zx=24$, then find $x^2+y^2+z^2$.

Framing problem : Show that $\frac{x^2}{yz+1}+\frac{y^2}{zx+1}+\frac{z^2}{xy+1}\leq\frac{x^2+y^2+z^2}{4} +1$

If $a,b,c$ are the sides of a triangle, then $\dfrac{a}{b+c-a}+\dfrac{b}{c+a-b}+\dfrac{c}{a+b-c}$ is:

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