Question

Euclidean distance representation as a norm

score 519 · Answer 1 · 2019-03-13 20:03:30

519

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Euclidean distance representation as a norm

Published on 13 Mar 2019 - 20:03

score 434 · Answer 2 · 2026-03-27 15:17:54

434

Views

If $f$ is integrable, then $\| f\|$ is also integrable.

Published on 27 Mar 2026 - 15:17

score 51 · Answer 3 · 2026-03-30 12:04:18

51

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Find a matrix A that satisfies data

Published on 30 Mar 2026 - 12:04

score 215 · Answer 4 · 2026-03-25 17:24:33

215

Views

Does the series corresponding to a Cauchy sequence always converge absolutely?

Published on 25 Mar 2026 - 17:24

score 306 · Answer 5 · 2019-03-15 11:03:49

Prove euclidean norm property : $\Vert \lambda \mathbf{x} \Vert_2 = \vert \lambda \vert \cdot \Vert \mathbf{x} \Vert_2$

score 512 · Answer 6 · 2026-03-25 14:23:59

512

Views

Weak continuity of the addition and scalar multiplication

Published on 25 Mar 2026 - 14:23

score 179 · Answer 7 · 2019-03-15 13:30:40

179

Views

Topology. In the $\ell^2$ space. Is the following set compact, bounded and/or closed?

Published on 15 Mar 2019 - 13:30

score 65 · Answer 8 · 2019-03-15 14:30:30

65

Views

Is the norm $||x||:= \sum\limits_{i=1}^{\infty} 2^{-i}|x_i|$ equivalent to usual norm in $l_2$?

Published on 15 Mar 2019 - 14:30

score 142 · Answer 9 · 2019-03-15 23:01:15

142

Views

Suppose $U_1,\dots,U_k$ and $V_1,\dots,V_k$ are $n\times n$ unitary matrices. Show that $\|U_1\cdots U_k-V_1\cdots V_k\|\leq\sum_{i=1}^k\|U_i-V_i\|$

Published on 15 Mar 2019 - 23:01

score 125 · Answer 10 · 2019-03-16 06:45:29

125

Views

To what extent are measure, topology, distances / norms related?

Published on 16 Mar 2019 - 6:45

score 92 · Answer 11 · 2026-03-25 06:00:26

92

Views

When is $\|\boldsymbol A\| \|\boldsymbol A^{-1}\|$ bounded?

Published on 25 Mar 2026 - 6:00

score 28 · Answer 12 · 2026-03-25 09:53:48

28

Views

Can we calculate gaussian integrals using non-typical norms on R^2

Published on 25 Mar 2026 - 9:53

score 365 · Answer 13 · 2026-03-27 08:55:59

365

Views

Inequality of vector norms with projections

Published on 27 Mar 2026 - 8:55

score 339 · Answer 14 · 2026-03-28 01:35:13

339

Views

Proof of Cauchy-Schwartz inequality with dot product and euclidean norm

Published on 28 Mar 2026 - 1:35

score 57 · Answer 15 · 2026-03-24 23:44:59

57

Views

Example of a matrix where equality occurs for the relation between infinite and 2 norm

Published on 24 Mar 2026 - 23:44

List Question

Euclidean distance representation as a norm

If $f$ is integrable, then $\| f\|$ is also integrable.

Find a matrix A that satisfies data

Does the series corresponding to a Cauchy sequence always converge absolutely?

Prove euclidean norm property : $\Vert \lambda \mathbf{x} \Vert_2 = \vert \lambda \vert \cdot \Vert \mathbf{x} \Vert_2$

Weak continuity of the addition and scalar multiplication

Topology. In the $\ell^2$ space. Is the following set compact, bounded and/or closed?

Is the norm $||x||:= \sum\limits_{i=1}^{\infty} 2^{-i}|x_i|$ equivalent to usual norm in $l_2$?

Suppose $U_1,\dots,U_k$ and $V_1,\dots,V_k$ are $n\times n$ unitary matrices. Show that $\|U_1\cdots U_k-V_1\cdots V_k\|\leq\sum_{i=1}^k\|U_i-V_i\|$

To what extent are measure, topology, distances / norms related?

When is $\|\boldsymbol A\| \|\boldsymbol A^{-1}\|$ bounded?

Can we calculate gaussian integrals using non-typical norms on R^2

Inequality of vector norms with projections

Proof of Cauchy-Schwartz inequality with dot product and euclidean norm

Example of a matrix where equality occurs for the relation between infinite and 2 norm

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