Question

For nonzero $v, w\in\Bbb{R}^n$, prove a linear isometry exists s.t. $Tv=\|v\|e_1$, and $Tw\in\operatorname{span}\{e_1, e_2\}.$

score 52 · Answer 1 · 2020-03-21 21:45:12

52

Views

For nonzero $v, w\in\Bbb{R}^n$, prove a linear isometry exists s.t. $Tv=\|v\|e_1$, and $Tw\in\operatorname{span}\{e_1, e_2\}.$

Published on 21 Mar 2020 - 21:45

score 16 · Answer 2 · 2026-03-10 17:46:27

16

Views

Isometry of translation (does $x+v \mapsto y+v$)

Published on 10 Mar 2026 - 17:46

score 206 · Answer 3 · 2020-03-25 19:59:39

206

Views

Show that f is an isomorphism of metric spaces

Published on 25 Mar 2020 - 19:59

score 672 · Answer 4 · 2020-03-28 13:45:19

672

Views

Groups of glide reflections and translations

Published on 28 Mar 2020 - 13:45

score 34 · Answer 5 · 2020-03-29 14:14:37

34

Views

Can I translate this problem from $L_2(\Omega)$ to $\mathbb{R}^{n}$?

Published on 29 Mar 2020 - 14:14

score 118 · Answer 6 · 2020-04-01 09:43:43

118

Views

Name and representation of isometries in $\Bbb R ^4$

Published on 01 Apr 2020 - 9:43

score 368 · Answer 7 · 2020-04-04 03:58:28

368

Views

Are measurements using the first fundamental form preserved by re-parameterization?

Published on 04 Apr 2020 - 3:58

score 163 · Answer 8 · 2020-04-07 06:56:42

163

Views

Isometries and Symmetries of the set $\mathbb{Z}^2$ as a subset of $\mathbb{R}^2$

Published on 07 Apr 2020 - 6:56

score 2.9k · Answer 9 · 2020-04-09 13:05:36

2.9k

Views

How to show that the inverse of an isometry is also an isometry?

Published on 09 Apr 2020 - 13:05

score 200 · Answer 10 · 2020-04-15 02:56:13

200

Views

How to prove an isometry is injective?

Published on 15 Apr 2020 - 2:56

score 319 · Answer 11 · 2020-04-17 07:56:11

319

Views

Using homeomorphism to induce an equivalent metric.

Published on 17 Apr 2020 - 7:56

score 224 · Answer 12 · 2020-04-21 13:12:22

224

Views

Showing linear isometry

Published on 21 Apr 2020 - 13:12

score 83 · Answer 13 · 2020-04-23 06:04:14

83

Views

Is the topological space $ (X^{},\sigma (X ^ {}, X)) $ metrizable?

Published on 23 Apr 2020 - 6:04

score 493 · Answer 14 · 2020-04-23 21:29:29

493

Views

Conditions for local isometry to be a symmetric relation.

Published on 23 Apr 2020 - 21:29

score 30 · Answer 15 · 2020-04-25 17:39:23

30

Views

If $U$ is a linear isometry on $H$, then $\frac1n\left\|(1-U^n)x\right\|_H\xrightarrow{n\to\infty}0$

Published on 25 Apr 2020 - 17:39

List Question

For nonzero $v, w\in\Bbb{R}^n$, prove a linear isometry exists s.t. $Tv=\|v\|e_1$, and $Tw\in\operatorname{span}\{e_1, e_2\}.$

Isometry of translation (does $x+v \mapsto y+v$)

Show that f is an isomorphism of metric spaces

Groups of glide reflections and translations

Can I translate this problem from $L_2(\Omega)$ to $\mathbb{R}^{n}$?

Name and representation of isometries in $\Bbb R ^4$

Are measurements using the first fundamental form preserved by re-parameterization?

Isometries and Symmetries of the set $\mathbb{Z}^2$ as a subset of $\mathbb{R}^2$

How to show that the inverse of an isometry is also an isometry?

How to prove an isometry is injective?

Using homeomorphism to induce an equivalent metric.

Showing linear isometry

Is the topological space $ (X^{},\sigma (X ^ {}, X)) $ metrizable?

Conditions for local isometry to be a symmetric relation.

If $U$ is a linear isometry on $H$, then $\frac1n\left\|(1-U^n)x\right\|_H\xrightarrow{n\to\infty}0$

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