Question

Show that the $l^p$ norms with $1\leq p,q\leq \infty$ are equivalent

score 301 · Answer 1 · 2019-01-16 22:30:31

301

Views

Show that the $l^p$ norms with $1\leq p,q\leq \infty$ are equivalent

Published on 16 Jan 2019 - 22:30

score 69 · Answer 2 · 2026-03-26 09:49:31

69

Views

How does it conclude that sup-norm is not a field norm?

Published on 26 Mar 2026 - 9:49

score 426 · Answer 3 · 2019-01-17 18:25:57

426

Views

Triangle inequality for linear operators

Published on 17 Jan 2019 - 18:25

score 131 · Answer 4 · 2019-01-18 03:35:27

131

Views

Continuity of Energy Functional

Published on 18 Jan 2019 - 3:35

score 39 · Answer 5 · 2026-03-27 00:03:45

39

Views

Question regarding the algebra of norms

Published on 27 Mar 2026 - 0:03

score 26 · Answer 6 · 2026-03-25 09:28:21

26

Views

How to set number of pairings in relation to cost

Published on 25 Mar 2026 - 9:28

score 83 · Answer 7 · 2019-01-18 22:40:56

83

Views

If $\left\Vert A\right\Vert \geq c$ then $\left|\lambda\right|>c$ for all eigenvalues of $A$

Published on 18 Jan 2019 - 22:40

score 51 · Answer 8 · 2026-03-25 03:04:16

51

Views

Show $||U_i-V_i||\leq\epsilon\ \ \forall i=1,...,m\Longrightarrow||U_m...U_1-V_m...V_1||\leq m\epsilon$ (spectral norm)

Published on 25 Mar 2026 - 3:04

score 90 · Answer 9 · 2019-01-19 09:14:22

90

Views

$T$ is closed $\iff$ for arbitrary $\{ x_n \}\in D(T)$ such that $x_n\to x,$ and $Tx_n\to y,$ we have $x\in D(T)$ and $Tx=y.$

Published on 19 Jan 2019 - 9:14

score 99 · Answer 10 · 2019-01-19 12:37:22

99

Views

understanding part of proof in Banach-Steinhaus theorem

Published on 19 Jan 2019 - 12:37

score 239 · Answer 11 · 2019-01-19 12:45:18

239

Views

Is one norm property: $p(v)=0 \iff v=0$ or positive definiteness?

Published on 19 Jan 2019 - 12:45

score 77 · Answer 12 · 2019-01-19 14:25:57

77

Views

Is the norm $p(x) = \max_{t \in [0,2]}|x(t)| + \left(\int_0^1|x(t)|^7\right)^{1/7}$ on $C[0,2]$ induced by any scalar product?

Published on 19 Jan 2019 - 14:25

score 1.5k · Answer 13 · 2026-03-26 21:04:43

1.5k

Views

$\infty$-norm of a vector

Published on 26 Mar 2026 - 21:04

score 336 · Answer 14 · 2026-03-27 18:27:49

336

Views

Does Cauchy-Schwarz imply $|x^Ty| \leq \|x\|_p\|y\|_p$ for any $p \geq 1$?

Published on 27 Mar 2026 - 18:27

score 31 · Answer 15 · 2026-03-25 17:23:38

31

Views

Finding Objects Most Similar to Other Objects as a "Linear Combination"

Published on 25 Mar 2026 - 17:23

List Question

Show that the $l^p$ norms with $1\leq p,q\leq \infty$ are equivalent

How does it conclude that sup-norm is not a field norm?

Triangle inequality for linear operators

Continuity of Energy Functional

Question regarding the algebra of norms

How to set number of pairings in relation to cost

If $\left\Vert A\right\Vert \geq c$ then $\left|\lambda\right|>c$ for all eigenvalues of $A$

Show $||U_i-V_i||\leq\epsilon\ \ \forall i=1,...,m\Longrightarrow||U_m...U_1-V_m...V_1||\leq m\epsilon$ (spectral norm)

$T$ is closed $\iff$ for arbitrary $\{ x_n \}\in D(T)$ such that $x_n\to x,$ and $Tx_n\to y,$ we have $x\in D(T)$ and $Tx=y.$

understanding part of proof in Banach-Steinhaus theorem

Is one norm property: $p(v)=0 \iff v=0$ or positive definiteness?

Is the norm $p(x) = \max_{t \in [0,2]}|x(t)| + \left(\int_0^1|x(t)|^7\right)^{1/7}$ on $C[0,2]$ induced by any scalar product?

$\infty$-norm of a vector

Does Cauchy-Schwarz imply $|x^Ty| \leq \|x\|_p\|y\|_p$ for any $p \geq 1$?

Finding Objects Most Similar to Other Objects as a "Linear Combination"

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