Question

Finding vectors $\mathbf{z}_i$ such that a matrix of scalar products has full rank for all $\mathbf{x}$, $\mathbf{y}$ l.i.

score 41 · Answer 1 · 2020-11-17 18:03:35

41

Views

Finding vectors $\mathbf{z}_i$ such that a matrix of scalar products has full rank for all $\mathbf{x}$, $\mathbf{y}$ l.i.

Published on 17 Nov 2020 - 18:03

score 3.5k · Answer 2 · 2026-03-29 06:29:04

3.5k

Views

What does it mean that a Jacobian matrix has full rank in an optimisation problem?

Published on 29 Mar 2026 - 6:29

score 229 · Answer 3 · 2026-03-29 19:50:08

229

Views

What is the tangent cone of the set of low-rank positive semidefinite matrices?

Published on 29 Mar 2026 - 19:50

score 3.1k · Answer 4 · 2020-11-22 11:38:16

3.1k

Views

Prove that if $x^TAx = 0 \Rightarrow Ax = 0$

Published on 22 Nov 2020 - 11:38

score 101 · Answer 5 · 2020-11-24 01:37:30

101

Views

Is it possible to construct matrices $A$ and $B$ such that $AB$ is invertible?

Published on 24 Nov 2020 - 1:37

score 835 · Answer 6 · 2020-11-26 12:45:26

835

Views

Rank and Dimension of Kernel for non-square matrix

Published on 26 Nov 2020 - 12:45

score 189 · Answer 7 · 2020-11-27 21:54:30

189

Views

Can a given symmetric matrix be written as a linear combination of the identity and a rank-$1$ matrix?

Published on 27 Nov 2020 - 21:54

score 683 · Answer 8 · 2020-11-28 16:05:21

683

Views

Show that rank($A^{n+1}$) = rank($A^n$)

Published on 28 Nov 2020 - 16:05

score 70 · Answer 9 · 2020-11-29 01:26:23

Finding basis and dimension depending on parameter for given vector subspace of $\mathbb{R}^n$ (have a solution but unsure of a few details)

score 39 · Answer 10 · 2020-11-30 16:06:11

39

Views

There's an arrangement of vectors in linear space V over the field K. Is it possible that the field $lin(A)$ is infinitely dimensional?

Published on 30 Nov 2020 - 16:06

score 264 · Answer 11 · 2020-11-30 21:08:38

264

Views

rank of a matrix if one component of each row is a linear combination of the others

Published on 30 Nov 2020 - 21:08

score 358 · Answer 12 · 2020-12-01 07:58:26

358

Views

Let A be an mxn matrix of rank 1. Using the definition of rank, show that there exists an mx1 matrix X and an 1xn matrix Y such that A=XY

Published on 01 Dec 2020 - 7:58

score 412 · Answer 13 · 2020-12-01 16:23:21

412

Views

Finding the rank and dimker of a matrix.

Published on 01 Dec 2020 - 16:23

score 42 · Answer 14 · 2020-12-02 13:28:51

42

Views

$AB-AA^TABB^TA^Tvv^TAB$ is not full rank

Published on 02 Dec 2020 - 13:28

score 54 · Answer 15 · 2020-12-04 09:22:53

54

Views

Full rankedness of the sum of two matrices satisfying a certain condition

Published on 04 Dec 2020 - 9:22

List Question

Finding vectors $\mathbf{z}_i$ such that a matrix of scalar products has full rank for all $\mathbf{x}$, $\mathbf{y}$ l.i.

What does it mean that a Jacobian matrix has full rank in an optimisation problem?

What is the tangent cone of the set of low-rank positive semidefinite matrices?

Prove that if $x^TAx = 0 \Rightarrow Ax = 0$

Is it possible to construct matrices $A$ and $B$ such that $AB$ is invertible?

Rank and Dimension of Kernel for non-square matrix

Can a given symmetric matrix be written as a linear combination of the identity and a rank-$1$ matrix?

Show that rank($A^{n+1}$) = rank($A^n$)

Finding basis and dimension depending on parameter for given vector subspace of $\mathbb{R}^n$ (have a solution but unsure of a few details)

There's an arrangement of vectors in linear space V over the field K. Is it possible that the field $lin(A)$ is infinitely dimensional?

rank of a matrix if one component of each row is a linear combination of the others

Let A be an mxn matrix of rank 1. Using the definition of rank, show that there exists an mx1 matrix X and an 1xn matrix Y such that A=XY

Finding the rank and dimker of a matrix.

$AB-AA^TABB^TA^Tvv^TAB$ is not full rank

Full rankedness of the sum of two matrices satisfying a certain condition

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