List questions from cauchy-schwarz-inequality

Published on 23 Feb 2026 - 4:21

47

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Polar set of $S=\{s\in\mathbb{R}^n:1^Ts≤1,\; s≥0\}$

Published on 17 May 2020 - 18:03

20

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Inequality about two inner product?

Published on 18 May 2020 - 15:59

112

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Cauchy Schwarz for 3 sequences of terms?

Published on 20 May 2020 - 4:15

138

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Prove $(a+b+c)^3 (a+b-c)(b+c-a)(c+a-b) \leqq 27a^2 b^ 2 c^2$

Published on 25 Mar 2026 - 16:02

52

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How to show that $\sum_{i=1}^{k}\sum_{j=0}^{n-1}x_{i,j}^{2} = \frac{k}{n}$ iff $x_{i,j}=\frac{1}{n} \forall i,j$ when $\sum_{j=0}^{n-1}x_{i,j}=1$

Published on 21 May 2020 - 22:16

34

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Find the Infimum and supremum of the following sum.

Published on 24 May 2020 - 0:05

82

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Using Holder and C-S to prove the radical inequality.

Published on 25 Mar 2026 - 16:21

152

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A strange inequality

Published on 28 Mar 2026 - 8:48

866

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Let $T:\textbf{R}^{n}\to\textbf{R}^{m}$ be a linear transformation. Show that there exists a number $M > 0$ such that $\|Tx\|\leq M\|x\|$.

Published on 25 May 2020 - 18:26

72

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For Euclidean vectors $x_1,\ldots,x_n$ with $\|x_i-x_j\|\geq 2$ for $i\neq j$, show $\sup_{i\in\{1,\ldots,n\} }\|x_i\|\geq \sqrt{2(n-1)/n}$

Published on 25 May 2020 - 19:06

194

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Prove that $\left(\dfrac{b}{a}+\dfrac{d}{c}\right)\cdot\left(\dfrac{a}{b}+\dfrac{c}{d}\right)\geq4$ with $a>0, b>0 , c> 0$ and $d>0.$

Published on 28 Mar 2026 - 8:50

76

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Proof Check of this Theorem in Metric Spaces

Published on 26 May 2020 - 11:19

112

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Prove $(a+b)\left(\frac{1}{a}+\frac{4}{b}\right)\geq9$ with $a>0$ and $b > 0$. When does equality hold?

Published on 26 May 2020 - 16:13

59

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How to prove inequality $(2n-1)x^{-1} + (2n+1)x^{2n-1} > \frac{(2n+1)^2}{2n}, \quad n > 2$ and $ 0 < x < 1$

Published on 28 Mar 2026 - 8:50

List Question

Prove $\sum \sqrt{3a+\frac{1}{b}} \geq 6$

Polar set of $S=\{s\in\mathbb{R}^n:1^Ts≤1,\; s≥0\}$

Inequality about two inner product?

Cauchy Schwarz for 3 sequences of terms?

Prove $(a+b+c)^3 (a+b-c)(b+c-a)(c+a-b) \leqq 27a^2 b^ 2 c^2$

How to show that $\sum_{i=1}^{k}\sum_{j=0}^{n-1}x_{i,j}^{2} = \frac{k}{n}$ iff $x_{i,j}=\frac{1}{n} \forall i,j$ when $\sum_{j=0}^{n-1}x_{i,j}=1$

Find the Infimum and supremum of the following sum.

Using Holder and C-S to prove the radical inequality.

A strange inequality

Let $T:\textbf{R}^{n}\to\textbf{R}^{m}$ be a linear transformation. Show that there exists a number $M > 0$ such that $\|Tx\|\leq M\|x\|$.

For Euclidean vectors $x_1,\ldots,x_n$ with $\|x_i-x_j\|\geq 2$ for $i\neq j$, show $\sup_{i\in\{1,\ldots,n\} }\|x_i\|\geq \sqrt{2(n-1)/n}$

Prove that $\left(\dfrac{b}{a}+\dfrac{d}{c}\right)\cdot\left(\dfrac{a}{b}+\dfrac{c}{d}\right)\geq4$ with $a>0, b>0 , c> 0$ and $d>0.$

Proof Check of this Theorem in Metric Spaces

Prove $(a+b)\left(\frac{1}{a}+\frac{4}{b}\right)\geq9$ with $a>0$ and $b > 0$. When does equality hold?

How to prove inequality $(2n-1)x^{-1} + (2n+1)x^{2n-1} > \frac{(2n+1)^2}{2n}, \quad n > 2$ and $ 0 < x < 1$

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