Question

Prove that $\text{tr}(B_1^{-1} B_2) \geq \text{tr}((A^\text{T} B_1 A)^{+} A^\text{T} B_2 A)$

score 59 · Answer 1 · 2023-12-05 08:20:50

59

Views

Prove that $\text{tr}(B_1^{-1} B_2) \geq \text{tr}((A^\text{T} B_1 A)^{+} A^\text{T} B_2 A)$

Published on 05 Dec 2023 - 8:20

score 40 · Answer 2 · 2023-12-23 22:25:04

40

Views

Describe any vector $x$ that has uniform inner product with every vector in the given set.

Published on 23 Dec 2023 - 22:25

score 56 · Answer 3 · 2023-12-26 16:03:05

56

Views

Prove that the Moore-Penrose inverse of a symmetric matrix have the same nullspace as the original.

Published on 26 Dec 2023 - 16:03

score 51 · Answer 4 · 2026-02-23 00:48:13

51

Views

Continuity Properties of Pseudoinverse with Orthogonal Block

Published on 23 Feb 2026 - 0:48

score 51 · Answer 5 · 2024-01-03 03:16:00

51

Views

Solving a matrix optimization problem

Published on 03 Jan 2024 - 3:16

score 23 · Answer 6 · 2024-01-05 06:41:56

23

Views

Solving a matrix optimization problem (part 2)

Published on 05 Jan 2024 - 6:41

score 44 · Answer 7 · 2024-01-08 10:48:00

44

Views

Orthogonal projection on a lower triangular non square block matrix $A \in \mathbb R^{m=4k,n=7k}$ such that $A_{i,j}\in \{0,1\}$

Published on 08 Jan 2024 - 10:48

score 117 · Answer 8 · 2024-01-12 11:41:59

117

Views

Given a $n \times n$ matrix $A$, when do the first $p$ columns of $A^{-1}$ coincide with the Moore–Penrose inverse of the first $p$ rows of $A$?

Published on 12 Jan 2024 - 11:41

score 140 · Answer 9 · 2024-01-25 13:06:25

140

Views

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

Published on 25 Jan 2024 - 13:06

score 107 · Answer 10 · 2024-02-04 20:26:53

107

Views

For what vectors does $A^+ A v = v$, where $A^+$ is the Moore-Penrose pseudoinverseof $A$?

Published on 04 Feb 2024 - 20:26

score 37 · Answer 11 · 2026-03-18 00:43:13

37

Views

Question related to splitting of matrix

Published on 18 Mar 2026 - 0:43

score 18 · Answer 12 · 2024-02-29 20:20:20

18

Views

What is the property of matrix $S$ to be near-identity matrix for $M$, e.g. $SM$ is close to $M$?

Published on 29 Feb 2024 - 20:20

score 18 · Answer 13 · 2026-03-19 12:10:18

18

Views

Pseudo-Inverse of mapping with identical null-spaces

Published on 19 Mar 2026 - 12:10

score 26 · Answer 14 · 2026-03-26 04:49:42

26

Views

Non-negative QP

Published on 26 Mar 2026 - 4:49

score 34 · Answer 15 · 2024-03-11 06:01:58

34

Views

Show that if the rows of matrix can be split into two orthogonal linear subspaces, then the inverse has each pseudoinverse as columns

Published on 11 Mar 2024 - 6:01

List Question

Prove that $\text{tr}(B_1^{-1} B_2) \geq \text{tr}((A^\text{T} B_1 A)^{+} A^\text{T} B_2 A)$

Describe any vector $x$ that has uniform inner product with every vector in the given set.

Prove that the Moore-Penrose inverse of a symmetric matrix have the same nullspace as the original.

Continuity Properties of Pseudoinverse with Orthogonal Block

Solving a matrix optimization problem

Solving a matrix optimization problem (part 2)

Orthogonal projection on a lower triangular non square block matrix $A \in \mathbb R^{m=4k,n=7k}$ such that $A_{i,j}\in \{0,1\}$

Given a $n \times n$ matrix $A$, when do the first $p$ columns of $A^{-1}$ coincide with the Moore–Penrose inverse of the first $p$ rows of $A$?

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

For what vectors does $A^+ A v = v$, where $A^+$ is the Moore-Penrose pseudoinverseof $A$?

Question related to splitting of matrix

What is the property of matrix $S$ to be near-identity matrix for $M$, e.g. $SM$ is close to $M$?

Pseudo-Inverse of mapping with identical null-spaces

Non-negative QP

Show that if the rows of matrix can be split into two orthogonal linear subspaces, then the inverse has each pseudoinverse as columns

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