Question

Show that if $\beta \mid \alpha$ in $\mathbb Z[i]$ then $N(\beta) \mid N(\alpha)$

score 239 · Answer 1 · 2026-03-25 06:03:17

239

Views

Show that if $\beta \mid \alpha$ in $\mathbb Z[i]$ then $N(\beta) \mid N(\alpha)$

Published on 25 Mar 2026 - 6:03

score 81 · Answer 2 · 2026-03-28 15:26:22

81

Views

Can we approximate a function $f\in L^1$ by a function $g\in L^2$ in $L^2$ norm?

Published on 28 Mar 2026 - 15:26

score 56 · Answer 3 · 2018-08-25 09:24:29

56

Views

What is $\|P\|_\infty $ or $\|P\|_p$ for a polynomial?

Published on 25 Aug 2018 - 9:24

score 268 · Answer 4 · 2026-03-28 00:54:14

268

Views

Convex Optimization Problem - Least Squares with Euclidean Norm Inequality

Published on 28 Mar 2026 - 0:54

score 245 · Answer 5 · 2018-08-25 23:14:09

245

Views

Prove or disprove: For any $v\in\mathbb{R}^n, \|v\|_1\|v\|_\infty \leq \frac{1+\sqrt{n}}{2}\|v\|_2^2$

Published on 25 Aug 2018 - 23:14

score 29 · Answer 6 · 2018-08-26 08:27:27

29

Views

Achievability under arbitrary norm

Published on 26 Aug 2018 - 8:27

score 192 · Answer 7 · 2026-03-27 08:40:03

192

Views

matrix inequality upper bound $\|A(B+C) +D(B-C)\|/2$?

Published on 27 Mar 2026 - 8:40

score 122 · Answer 8 · 2018-08-27 14:24:37

122

Views

A symmetry identity involving norms

Published on 27 Aug 2018 - 14:24

score 15 · Answer 9 · 2026-03-06 17:22:33

15

Views

Proving the relationship between 2 intervals

Published on 06 Mar 2026 - 17:22

score 564 · Answer 10 · 2026-03-30 02:11:33

564

Views

Convex conjugate of the composition of a norm with a convex function

Published on 30 Mar 2026 - 2:11

score 147 · Answer 11 · 2026-03-25 02:59:35

147

Views

Norm on hyperreals ${^*\mathbb R}$ using the ultrafilter construction

Published on 25 Mar 2026 - 2:59

score 58 · Answer 12 · 2018-08-28 12:21:26

58

Views

Global minimum of $f(x)=\sum_{v=1}^k m_v\|x-x_v\|_2^2, \ \ \ x,x_v \in \mathbb{R}^n, m_v \in \mathbb{R}>0$

Published on 28 Aug 2018 - 12:21

score 503 · Answer 13 · 2026-03-25 09:49:25

503

Views

Dual space of $R^n$ with $\max$ norm

Published on 25 Mar 2026 - 9:49

score 42 · Answer 14 · 2026-03-26 02:57:40

42

Views

Let $A: \Bbb{R}^{+}\to M_{n\times n}(\Bbb{R})$, then $A(t)$ is continuous if and only if $a_{ij}(t)$ is continuous, $\forall\;i,j=1,\cdots,n$

Published on 26 Mar 2026 - 2:57

score 98 · Answer 15 · 2018-08-28 20:47:06

98

Views

Linear and continuous applications (normed space)

Published on 28 Aug 2018 - 20:47

List Question

Show that if $\beta \mid \alpha$ in $\mathbb Z[i]$ then $N(\beta) \mid N(\alpha)$

Can we approximate a function $f\in L^1$ by a function $g\in L^2$ in $L^2$ norm?

What is $\|P\|_\infty $ or $\|P\|_p$ for a polynomial?

Convex Optimization Problem - Least Squares with Euclidean Norm Inequality

Prove or disprove: For any $v\in\mathbb{R}^n, \|v\|_1\|v\|_\infty \leq \frac{1+\sqrt{n}}{2}\|v\|_2^2$

Achievability under arbitrary norm

matrix inequality upper bound $\|A(B+C) +D(B-C)\|/2$?

A symmetry identity involving norms

Proving the relationship between 2 intervals

Convex conjugate of the composition of a norm with a convex function

Norm on hyperreals ${^*\mathbb R}$ using the ultrafilter construction

Global minimum of $f(x)=\sum_{v=1}^k m_v\|x-x_v\|_2^2, \ \ \ x,x_v \in \mathbb{R}^n, m_v \in \mathbb{R}>0$

Dual space of $R^n$ with $\max$ norm

Let $A: \Bbb{R}^{+}\to M_{n\times n}(\Bbb{R})$, then $A(t)$ is continuous if and only if $a_{ij}(t)$ is continuous, $\forall\;i,j=1,\cdots,n$

Linear and continuous applications (normed space)

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