Question

Linearly independence of functions without using Wronskian

score 107 · Answer 1 · 2021-09-01 23:36:15

107

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Linearly independence of functions without using Wronskian

Published on 01 Sep 2021 - 23:36

score 211 · Answer 2 · 2021-09-02 01:35:05

211

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Rank of product of matrices: $\operatorname{rank}(ABA') = \operatorname{rank}(A)$ when $\operatorname{rank}(A) = \operatorname{rank}(B)$

Published on 02 Sep 2021 - 1:35

score 49 · Answer 3 · 2026-03-25 17:21:50

49

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Why is the boundary of spectrahedra “more pointy” at matrices of lower rank?

Published on 25 Mar 2026 - 17:21

score 160 · Answer 4 · 2021-09-05 04:05:21

160

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Prove or disprove there exists a permutation \sigma such that the (i,\sigma(i))th minor and the (i,\sigma(i))th entry of M are both nonzero for each i

Published on 05 Sep 2021 - 4:05

score 126 · Answer 5 · 2021-09-07 03:33:07

126

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If $A$ and $B$ have independent columns, prove that $B^TA$ is invertible

Published on 07 Sep 2021 - 3:33

score 86 · Answer 6 · 2021-09-10 18:36:48

86

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$V=W\oplus U=U\oplus X=W\oplus X$. Show there is a $2$ dim subspace $A\subseteq V$ s.t. each of $A\cap W, A\cap U$ and $A\cap X$ has dimension $1$.

Published on 10 Sep 2021 - 18:36

score 420 · Answer 7 · 2021-09-14 02:18:20

420

Views

How span of a set containing matrix row is related to the matrix rank?

Published on 14 Sep 2021 - 2:18

score 44 · Answer 8 · 2021-09-17 12:40:44

44

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Prove a particular matrix is invertible with high probability as the field size goes to infinity

Published on 17 Sep 2021 - 12:40

score 74 · Answer 9 · 2021-09-18 02:06:53

74

Views

Prove $\mathrm{rank}(B^T B) = \mathrm{rank}(B) = \mathrm{rank}(B^T )$.

Published on 18 Sep 2021 - 2:06

score 70 · Answer 10 · 2021-09-18 04:22:25

70

Views

Rank of a square matrix of order $7$.

Published on 18 Sep 2021 - 4:22

score 138 · Answer 11 · 2021-09-20 13:11:22

138

Views

The rank nullity theorem

Published on 20 Sep 2021 - 13:11

score 127 · Answer 12 · 2021-09-20 15:20:11

127

Views

Problem on rank of a matrix-Mathematics Competition

Published on 20 Sep 2021 - 15:20

score 398 · Answer 13 · 2026-02-23 10:48:58

398

Views

$3 \times3$ matrices with rank $1$ or $2$ are manifolds

Published on 23 Feb 2026 - 10:48

score 35 · Answer 14 · 2021-09-27 20:48:29

35

Views

Implications between $A$, $B$, $[A,B]^T$ having full column rank where $A$ and $B$ have less columns than rows

Published on 27 Sep 2021 - 20:48

score 185 · Answer 15 · 2021-09-28 17:13:35

185

Views

Transforming a matrix to obtain linear independent columns

Published on 28 Sep 2021 - 17:13

List Question

Linearly independence of functions without using Wronskian

Rank of product of matrices: $\operatorname{rank}(ABA') = \operatorname{rank}(A)$ when $\operatorname{rank}(A) = \operatorname{rank}(B)$

Why is the boundary of spectrahedra “more pointy” at matrices of lower rank?

Prove or disprove there exists a permutation \sigma such that the (i,\sigma(i))th minor and the (i,\sigma(i))th entry of M are both nonzero for each i

If $A$ and $B$ have independent columns, prove that $B^TA$ is invertible

$V=W\oplus U=U\oplus X=W\oplus X$. Show there is a $2$ dim subspace $A\subseteq V$ s.t. each of $A\cap W, A\cap U$ and $A\cap X$ has dimension $1$.

How span of a set containing matrix row is related to the matrix rank?

Prove a particular matrix is invertible with high probability as the field size goes to infinity

Prove $\mathrm{rank}(B^T B) = \mathrm{rank}(B) = \mathrm{rank}(B^T )$.

Rank of a square matrix of order $7$.

The rank nullity theorem

Problem on rank of a matrix-Mathematics Competition

$3 \times3$ matrices with rank $1$ or $2$ are manifolds

Implications between $A$, $B$, $[A,B]^T$ having full column rank where $A$ and $B$ have less columns than rows

Transforming a matrix to obtain linear independent columns

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