Question

Are there any refinements of $\langle \vec x,\vec y\rangle \leq \lVert \vec x\rVert_1\lVert \vec y\rVert_\infty$?

score 28 · Answer 1 · 2026-03-25 06:12:40

28

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Are there any refinements of $\langle \vec x,\vec y\rangle \leq \lVert \vec x\rVert_1\lVert \vec y\rVert_\infty$?

Published on 25 Mar 2026 - 6:12

score 90 · Answer 2 · 2026-03-27 14:02:24

90

Views

A variant of Cauchy-Schwarz Inequality for integral

Published on 27 Mar 2026 - 14:02

score 43 · Answer 3 · 2023-02-07 09:24:02

43

Views

How to calculate expectation bound?

Published on 07 Feb 2023 - 9:24

score 255 · Answer 4 · 2026-03-25 12:28:15

255

Views

Inequality $\frac{a^3}{3ab^2+2c^3} +\frac{b^3}{3bc^2+2a^3} +\frac{c^3}{3ca^2+2b^3} \geq \frac{3}{5} $

Published on 25 Mar 2026 - 12:28

score 103 · Answer 5 · 2026-03-25 20:34:09

103

Views

Pulling out a maximum term from an integral

Published on 25 Mar 2026 - 20:34

score 115 · Answer 6 · 2026-03-25 23:42:20

115

Views

I want to prove for all $a > 0 $, $b > 0$, $\frac{2ab}{a + b} + \sqrt{\frac{1}{2}\left(a^2 + b^2\right)} \geq \frac{a + b}{2} + \sqrt{ab}$

Published on 25 Mar 2026 - 23:42

score 95 · Answer 7 · 2026-03-25 22:03:45

95

Views

Trace inequality of Hadmard product

Published on 25 Mar 2026 - 22:03

score 161 · Answer 8 · 2026-03-30 00:21:05

161

Views

Largest $k$ such that $k \operatorname{Tr} H^2 C \le (\operatorname{Tr} H C)^2$

Published on 30 Mar 2026 - 0:21

score 115 · Answer 9 · 2026-03-27 01:44:05

115

Views

Cauchy-Schwarz inequality for matrices

Published on 27 Mar 2026 - 1:44

score 84 · Answer 10 · 2023-02-25 10:26:11

84

Views

Prove that $\int_{\mathbb{R}^3} f(x, y)g(y, z)h(z, x) dλ_3(x, y, z) ≤ ∥f∥_{L_2(\mathbb{R}^2 )}∥g∥_{L_2(\mathbb{R}^2 )}∥h∥_{L_2(\mathbb{R}^2 )}$

Published on 25 Feb 2023 - 10:26

score 112 · Answer 11 · 2026-02-23 06:21:57

112

Views

Proving that $\lVert x\rVert=\sqrt{\langle x,x \rangle}$ is a norm (triangle inequality).

Published on 23 Feb 2026 - 6:21

score 87 · Answer 12 · 2023-03-01 01:55:57

87

Views

Prove the The Cauchy--Schwarz--Buniakowski inequality using the fact that $E[X]^2 \le E[X^2]$.

Published on 01 Mar 2023 - 1:55

score 52 · Answer 13 · 2023-03-01 22:36:51

52

Views

I've been struggling with this method of proving $E[X^2] > E[X]^2$.

Published on 01 Mar 2023 - 22:36

score 40 · Answer 14 · 2026-03-26 03:00:20

40

Views

Pigeonhole coloring bound

Published on 26 Mar 2026 - 3:00

score 59 · Answer 15 · 2023-03-07 14:58:06

59

Views

Bounding $L^2$ operator norm of integral kernel

Published on 07 Mar 2023 - 14:58

List Question

Are there any refinements of $\langle \vec x,\vec y\rangle \leq \lVert \vec x\rVert_1\lVert \vec y\rVert_\infty$?

A variant of Cauchy-Schwarz Inequality for integral

How to calculate expectation bound?

Inequality $\frac{a^3}{3ab^2+2c^3} +\frac{b^3}{3bc^2+2a^3} +\frac{c^3}{3ca^2+2b^3} \geq \frac{3}{5} $

Pulling out a maximum term from an integral

I want to prove for all $a > 0 $, $b > 0$, $\frac{2ab}{a + b} + \sqrt{\frac{1}{2}\left(a^2 + b^2\right)} \geq \frac{a + b}{2} + \sqrt{ab}$

Trace inequality of Hadmard product

Largest $k$ such that $k \operatorname{Tr} H^2 C \le (\operatorname{Tr} H C)^2$

Cauchy-Schwarz inequality for matrices

Prove that $\int_{\mathbb{R}^3} f(x, y)g(y, z)h(z, x) dλ_3(x, y, z) ≤ ∥f∥_{L_2(\mathbb{R}^2 )}∥g∥_{L_2(\mathbb{R}^2 )}∥h∥_{L_2(\mathbb{R}^2 )}$

Proving that $\lVert x\rVert=\sqrt{\langle x,x \rangle}$ is a norm (triangle inequality).

Prove the The Cauchy--Schwarz--Buniakowski inequality using the fact that $E[X]^2 \le E[X^2]$.

I've been struggling with this method of proving $E[X^2] > E[X]^2$.

Pigeonhole coloring bound

Bounding $L^2$ operator norm of integral kernel

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