List questions from normed-spaces

Published on 11 Apr 2026 - 19:50

28

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Show that for every $A\in M_{n}(\mathbb{R})$ with rank(A)=1 that $||A||_{op}=||A||_{HS}$. What happens in the general case?

Published on 13 Apr 2026 - 21:59

480

Views

What type of set is the intersection of two spheres?

Published on 15 Apr 2026 - 20:36

36

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Can we prove that $\|uv^*\|_2 \leq 1$?

Published on 14 Apr 2026 - 15:30

43

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Difficulty in understanding the proof for convergence

Published on 08 Apr 2026 - 22:03

5.1k

Views

Trace distance remaining invariant under Unitary transformations

Published on 14 Apr 2026 - 12:00

961

Views

Is the subset of all sequences with finite number of non-zero entries a closed subspace of $l^2$?

Published on 16 Apr 2026 - 3:47

84

Views

I need help proving a matrix norm inequality

Published on 12 Apr 2026 - 4:31

70

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Find the tightest upper bound of $\sum\limits_{j = 1}^n v_j^2 w_j \leq C\sum\limits_{j = 1}^n v_j^2$

Published on 15 Apr 2026 - 9:19

140

Views

two definitions of isometry

Published on 09 Apr 2026 - 2:26

6.2k

Views

Frobenius Norm, Triangle inequality, and complex conjugates

Published on 10 Apr 2026 - 1:46

2.6k

Views

Dot product is an Euclidean norm in Euclidean space?

Published on 11 Apr 2026 - 17:31

202

Views

If $M$ is convex, prove that $M^\circ$ and $\bar M$ are convex

Published on 14 Apr 2026 - 10:41

258

Views

Dual of $l_\infty$

Published on 11 Apr 2026 - 12:39

53

Views

Induced Matrix Norms

Published on 09 Apr 2026 - 12:54

List Question

Norm in the space of absolutely convergent Fourier series

Show that for every $A\in M_{n}(\mathbb{R})$ with rank(A)=1 that $||A||_{op}=||A||_{HS}$. What happens in the general case?

What type of set is the intersection of two spheres?

Can we prove that $\|uv^*\|_2 \leq 1$?

Difficulty in understanding the proof for convergence

Trace distance remaining invariant under Unitary transformations

Is the subset of all sequences with finite number of non-zero entries a closed subspace of $l^2$?

I need help proving a matrix norm inequality

Find the tightest upper bound of $\sum\limits_{j = 1}^n v_j^2 w_j \leq C\sum\limits_{j = 1}^n v_j^2$

two definitions of isometry

Frobenius Norm, Triangle inequality, and complex conjugates

Dot product is an Euclidean norm in Euclidean space?

If $M$ is convex, prove that $M^\circ$ and $\bar M$ are convex

Dual of $l_\infty$

Induced Matrix Norms

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