Question

$A \in \mathbb{R}^{n \times n}$ is a symmetric, PSD matrix. I want to write $\|A\|_F$ as a function of the eigenvalues of $A$

score 790 · Answer 1 · 2026-03-26 11:01:43

790

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$A \in \mathbb{R}^{n \times n}$ is a symmetric, PSD matrix. I want to write $\|A\|_F$ as a function of the eigenvalues of $A$

Published on 26 Mar 2026 - 11:01

score 452 · Answer 2 · 2026-04-14 14:20:39

452

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Pasting Lemma (Topology munkres)

Published on 14 Apr 2026 - 14:20

score 61 · Answer 3 · 2026-04-10 17:20:45

61

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How does this show non-uniqueness?

Published on 10 Apr 2026 - 17:20

score 251 · Answer 4 · 2026-03-25 14:25:21

251

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Prove that $\int_1^a \frac{T_n(x) T_n(x/a)}{\sqrt{a^2 - x^2} \sqrt{x^2 - 1^2}} \frac{a}{x} \mathrm{d}x = \frac{\pi}{2}$

Published on 25 Mar 2026 - 14:25

score 55 · Answer 5 · 2026-04-09 16:42:04

55

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How to prove $A$ is equivalent to $B$?

Published on 09 Apr 2026 - 16:42

score 165 · Answer 6 · 2026-04-17 14:31:39

165

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Proof by induction:$\frac{3}{5}\cdot\frac{7}{9}\cdot\frac{11}{13}\cdots\frac{4n-1}{4n+1}<\sqrt{\frac{3}{4n+3}}$

Published on 17 Apr 2026 - 14:31

score 71 · Answer 7 · 2026-04-15 18:42:47

71

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2006 IMO Shortlist Questions A1 proof?

Published on 15 Apr 2026 - 18:42

score 84 · Answer 8 · 2026-04-15 23:57:26

max number of elements in a sequence where each $p$ consecutive subsequence sum is negative and $q$ consecutive subsequence sums is positive

score 64 · Answer 9 · 2026-04-24 12:53:44

64

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A detailed proof required.

Published on 24 Apr 2026 - 12:53

score 47 · Answer 10 · 2026-04-10 17:38:08

47

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Do we need a subbase for topologizing a target?

Published on 10 Apr 2026 - 17:38

score 59 · Answer 11 · 2026-04-13 04:30:51

59

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Constructing a bijection isomorphic to clopen subsets of $X..$

Published on 13 Apr 2026 - 4:30

score 1.5k · Answer 12 · 2026-04-26 07:50:14

1.5k

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On proving that a finitely generated group has a finite number of subgroups with index $n$.

Published on 26 Apr 2026 - 7:50

score 58 · Answer 13 · 2026-04-11 21:19:15

58

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How to prove this set is a Cantor set?

Published on 11 Apr 2026 - 21:19

score 28 · Answer 14 · 2026-04-17 15:12:57

28

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Show that a sequence can't be longer than $p+q-d$ when the product of every consecutive subsequence of length $p$ is $<1$ and $q$ products are $>1$

Published on 17 Apr 2026 - 15:12

score 374 · Answer 15 · 2026-04-16 22:44:28

374

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Euler characteristic of projective plane (rank$(H_1(\mathbb{R}P^2))=$ rank$(Z_2)=0?$)

Published on 16 Apr 2026 - 22:44

List Question

$A \in \mathbb{R}^{n \times n}$ is a symmetric, PSD matrix. I want to write $\|A\|_F$ as a function of the eigenvalues of $A$

Pasting Lemma (Topology munkres)

How does this show non-uniqueness?

Prove that $\int_1^a \frac{T_n(x) T_n(x/a)}{\sqrt{a^2 - x^2} \sqrt{x^2 - 1^2}} \frac{a}{x} \mathrm{d}x = \frac{\pi}{2}$

How to prove $A$ is equivalent to $B$?

Proof by induction:$\frac{3}{5}\cdot\frac{7}{9}\cdot\frac{11}{13}\cdots\frac{4n-1}{4n+1}<\sqrt{\frac{3}{4n+3}}$

2006 IMO Shortlist Questions A1 proof?

max number of elements in a sequence where each $p$ consecutive subsequence sum is negative and $q$ consecutive subsequence sums is positive

A detailed proof required.

Do we need a subbase for topologizing a target?

Constructing a bijection isomorphic to clopen subsets of $X..$

On proving that a finitely generated group has a finite number of subgroups with index $n$.

How to prove this set is a Cantor set?

Show that a sequence can't be longer than $p+q-d$ when the product of every consecutive subsequence of length $p$ is $<1$ and $q$ products are $>1$

Euler characteristic of projective plane (rank$(H_1(\mathbb{R}P^2))=$ rank$(Z_2)=0?$)

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