Question

rank of block lower triangular matrix

score 36 · Answer 1 · 2026-03-27 08:41:17

36

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rank of block lower triangular matrix

Published on 27 Mar 2026 - 8:41

score 57 · Answer 2 · 2026-03-27 04:00:05

57

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How is effective rank (a ratio of nuclear norm and operator norm) defined in terms of eigenvalues?

Published on 27 Mar 2026 - 4:00

score 141 · Answer 3 · 2026-03-26 21:12:42

141

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Solvability of $A X B=C$ with $X=X^\mathrm{T}$

Published on 26 Mar 2026 - 21:12

score 50 · Answer 4 · 2024-01-25 18:23:08

50

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Let A be an m by n matrix and let B be an n by p matrix. Show that rank A + nullity A = n is the special case of rank AB + dim(null A ∩ col B)=rank B.

Published on 25 Jan 2024 - 18:23

score 57 · Answer 5 · 2026-03-28 16:19:34

57

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Linear independence of binary vectors

Published on 28 Mar 2026 - 16:19

score 33 · Answer 6 · 2026-03-29 08:35:35

33

Views

How to find a matrix perturbation which lowers the rank of a matrix

Published on 29 Mar 2026 - 8:35

score 40 · Answer 7 · 2024-01-29 10:44:28

40

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$rank\begin{pmatrix}f(A)\\g(A)\end{pmatrix}=rank\begin{pmatrix}f(A)&g(A)\end{pmatrix}$?

Published on 29 Jan 2024 - 10:44

score 42 · Answer 8 · 2024-02-01 21:24:39

42

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Does $M = \sum_{k} \mathbf u_k \mathbf v_k^{\top}$ imply $\mathbf u_k \in \operatorname{colspan}(M)$?

Published on 01 Feb 2024 - 21:24

score 56 · Answer 9 · 2026-03-26 01:07:43

56

Views

Decide whether a 0-1 matrix has full rank

Published on 26 Mar 2026 - 1:07

score 103 · Answer 10 · 2024-02-10 14:29:47

103

Views

Implication of a certain matrix being full row rank regarding the rank of another matrix

Published on 10 Feb 2024 - 14:29

score 41 · Answer 11 · 2024-02-14 04:58:21

41

Views

Intuition behind pre-multiplication of a vector with a matrix

Published on 14 Feb 2024 - 4:58

score 50 · Answer 12 · 2024-02-14 20:57:04

50

Views

Computing the rank of a $3\times 3$ matrix with some restrictions

Published on 14 Feb 2024 - 20:57

score 17 · Answer 13 · 2024-02-19 19:03:51

17

Views

Are the columnspace and the nullspace not always the same for some matrix A (mxn) and some product of matrices BA, where B is invertible (mxm)?

Published on 19 Feb 2024 - 19:03

score 54 · Answer 14 · 2024-02-20 17:40:36

54

Views

Finding the entries in a matrix given that the rank has to be $2$

Published on 20 Feb 2024 - 17:40

score 56 · Answer 15 · 2026-03-28 07:51:45

56

Views

Prove $\ker(A+T(A))\subseteq \ker(A)$ for $A\geq 0$ and $T$ positive linear map

Published on 28 Mar 2026 - 7:51

List Question

rank of block lower triangular matrix

How is effective rank (a ratio of nuclear norm and operator norm) defined in terms of eigenvalues?

Solvability of $A X B=C$ with $X=X^\mathrm{T}$

Let A be an m by n matrix and let B be an n by p matrix. Show that rank A + nullity A = n is the special case of rank AB + dim(null A ∩ col B)=rank B.

Linear independence of binary vectors

How to find a matrix perturbation which lowers the rank of a matrix

$rank\begin{pmatrix}f(A)\\g(A)\end{pmatrix}=rank\begin{pmatrix}f(A)&g(A)\end{pmatrix}$?

Does $M = \sum_{k} \mathbf u_k \mathbf v_k^{\top}$ imply $\mathbf u_k \in \operatorname{colspan}(M)$?

Decide whether a 0-1 matrix has full rank

Implication of a certain matrix being full row rank regarding the rank of another matrix

Intuition behind pre-multiplication of a vector with a matrix

Computing the rank of a $3\times 3$ matrix with some restrictions

Are the columnspace and the nullspace not always the same for some matrix A (mxn) and some product of matrices BA, where B is invertible (mxm)?

Finding the entries in a matrix given that the rank has to be $2$

Prove $\ker(A+T(A))\subseteq \ker(A)$ for $A\geq 0$ and $T$ positive linear map

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