Question

What is the reasoning behind: $\sup_{\|y\|_{2} \leq 1} \theta \mathbf{x}^T \mathbf{y} = |\theta| \sup_{\|y\|_{2}\leq 1} {\mathbf{x}^T \mathbf{y}}$

score 30 · Answer 1 · 2017-10-02 02:00:55

What is the reasoning behind: $\sup_{\|y\|_{2} \leq 1} \theta \mathbf{x}^T \mathbf{y} = |\theta| \sup_{\|y\|_{2}\leq 1} {\mathbf{x}^T \mathbf{y}}$

score 7.8k · Answer 2 · 2017-10-02 19:01:18

7.8k

Views

Proof for sup and inf of $A=\{1-1/n:n\in\mathbb{N}\}⊂\mathbb{Q}$

Published on 02 Oct 2017 - 19:01

score 329 · Answer 3 · 2017-10-03 14:26:10

329

Views

Function defined as the supremum of a sequence of functions - epsilon-delta proofs

Published on 03 Oct 2017 - 14:26

score 793 · Answer 4 · 2017-10-03 15:02:26

793

Views

Function defined by infimum equals minimum

Published on 03 Oct 2017 - 15:02

score 77 · Answer 5 · 2017-10-04 17:01:20

77

Views

How do we know that $\sup$ exists for $\{w\in \Bbb R : b^w<y\}$

Published on 04 Oct 2017 - 17:01

score 336 · Answer 6 · 2017-10-04 20:41:59

336

Views

Supremum of the set of terms of the geometric series.

Published on 04 Oct 2017 - 20:41

score 21 · Answer 7 · 2017-10-04 21:26:39

21

Views

An interesting basic analysis exercise: looking for alternative solutions

Published on 04 Oct 2017 - 21:26

score 423 · Answer 8 · 2017-10-06 02:18:54

423

Views

Supremum of a Cumulative Distribution function

Published on 06 Oct 2017 - 2:18

score 21 · Answer 9 · 2017-10-06 05:23:05

21

Views

Let A be a non-empty set in R^k. Prove the inequality

Published on 06 Oct 2017 - 5:23

score 45 · Answer 10 · 2017-10-06 08:17:01

45

Views

Om which interval $I\in \mathbb{R}$ does $\sum_{k\geq 0} \sin^{k}(x)$ uniformly converge?

Published on 06 Oct 2017 - 8:17

score 72 · Answer 11 · 2017-10-06 12:02:57

72

Views

Subset of rationals with sup / without sup

Published on 06 Oct 2017 - 12:02

score 30 · Answer 12 · 2017-10-07 16:51:25

30

Views

How to show $\inf B$ is fixed point?

Published on 07 Oct 2017 - 16:51

score 433 · Answer 13 · 2017-10-07 18:40:04

433

Views

Infimum and supremum of set $A=\{\sqrt[n]{\frac{1}{n}}, n \in \mathbb{N}, n \ge 3 \}$

Published on 07 Oct 2017 - 18:40

score 191 · Answer 14 · 2017-10-07 19:29:14

191

Views

Let $S \subseteq \mathbb{R}$ have a supremum $x$. Show that there is a sequence $(x_n)$ in $S$ that converges to $x$.

Published on 07 Oct 2017 - 19:29

score 99 · Answer 15 · 2017-10-10 04:07:40

99

Views

Show that $\{|f''(z_0)|: f\in \mathcal{F}\}$ is a closed set for a compact family $ \mathcal{F}$ of holomorphic functions.

Published on 10 Oct 2017 - 4:07

List Question

What is the reasoning behind: $\sup_{\|y\|_{2} \leq 1} \theta \mathbf{x}^T \mathbf{y} = |\theta| \sup_{\|y\|_{2}\leq 1} {\mathbf{x}^T \mathbf{y}}$

Proof for sup and inf of $A=\{1-1/n:n\in\mathbb{N}\}⊂\mathbb{Q}$

Function defined as the supremum of a sequence of functions - epsilon-delta proofs

Function defined by infimum equals minimum

How do we know that $\sup$ exists for $\{w\in \Bbb R : b^w<y\}$

Supremum of the set of terms of the geometric series.

An interesting basic analysis exercise: looking for alternative solutions

Supremum of a Cumulative Distribution function

Let A be a non-empty set in R^k. Prove the inequality

Om which interval $I\in \mathbb{R}$ does $\sum_{k\geq 0} \sin^{k}(x)$ uniformly converge?

Subset of rationals with sup / without sup

How to show $\inf B$ is fixed point?

Infimum and supremum of set $A=\{\sqrt[n]{\frac{1}{n}}, n \in \mathbb{N}, n \ge 3 \}$

Let $S \subseteq \mathbb{R}$ have a supremum $x$. Show that there is a sequence $(x_n)$ in $S$ that converges to $x$.

Show that $\{|f''(z_0)|: f\in \mathcal{F}\}$ is a closed set for a compact family $ \mathcal{F}$ of holomorphic functions.

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