Question

Linear independence of $\begin{pmatrix}1\\ \vdots\\ \frac{1}{n}\end{pmatrix},\cdots,\begin{pmatrix}\frac{1}{n}\\ \vdots\\ \frac{1}{2n-1}\end{pmatrix}$

score 62 · Answer 1 · 2026-02-23 12:08:08

Linear independence of $\begin{pmatrix}1\\ \vdots\\ \frac{1}{n}\end{pmatrix},\cdots,\begin{pmatrix}\frac{1}{n}\\ \vdots\\ \frac{1}{2n-1}\end{pmatrix}$

score 76 · Answer 2 · 2026-02-23 12:08:05

76

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Prove: For full rank matrix $A\in\mathbb{C}^{m\times n}$ with $m>n$ and diagonal matrix $B\in\mathbb{C}^{n\times n}$ we have $rank(ABA^H)=n$

Published on 23 Feb 2026 - 12:08

score 54 · Answer 3 · 2026-02-23 12:01:18

54

Views

Gram Matrix and Linear Independence on Hilbert spaces source?

Published on 23 Feb 2026 - 12:01

score 35 · Answer 4 · 2026-02-23 12:09:17

35

Views

Contradiction between RREF & Determinant in evaluating Linear Independence

Published on 23 Feb 2026 - 12:09

score 95 · Answer 5 · 2026-02-23 12:09:15

95

Views

Find invertible matrices over a field such that the set of a vector multiplied by them is linearly independent

Published on 23 Feb 2026 - 12:09

score 45 · Answer 6 · 2026-02-23 12:09:15

45

Views

what is the quickest way of finding the set of all linearly independent sets over GF(2) and GF(3)?

Published on 23 Feb 2026 - 12:09

score 84 · Answer 7 · 2026-02-23 12:07:50

84

Views

Determine if a set of vectors is linearly independent or dependent?

Published on 23 Feb 2026 - 12:07

score 104 · Answer 8 · 2026-04-03 16:58:34

104

Views

What are some proofs that the list $1,z,...,z^m$ is linearly independent in $P(\mathbb{F})$ for each nonnegative integer $m$?

Published on 03 Apr 2026 - 16:58

score 40 · Answer 9 · 2026-02-23 12:02:59

40

Views

Linear independence of a matrix with only variables

Published on 23 Feb 2026 - 12:02

score 106 · Answer 10 · 2026-02-23 12:02:37

106

Views

Must linearly dependent vectors pass through the origin?

Published on 23 Feb 2026 - 12:02

score 168 · Answer 11 · 2026-02-23 12:07:49

168

Views

The $n\times n$ matrices $A^n, A^{n-1},\dots,\mathrm{id}_n$ are linearly dependent

Published on 23 Feb 2026 - 12:07

score 98 · Answer 12 · 2026-02-23 12:08:06

98

Views

How do we prove that $(x^4-6x^3), (x^3-6x^2), (x^2-6x)$, and $(x-6)$ are linearly independent?

Published on 23 Feb 2026 - 12:08

score 175 · Answer 13 · 2026-04-07 11:03:02

175

Views

If a vector in a linearly independent list is replaced by a linear combination of itself and one other vector is the result linearly independent?

Published on 07 Apr 2026 - 11:03

score 72 · Answer 14 · 2026-02-23 12:09:13

$u_{1},...,u_{n}\in V$ L.I.. Then for any $v_{1},...,v_{n}\in V$, $\exists$ infinitely $\alpha$ s.t. $u_{1}+\alpha v_{1},...,u_{n}+\alpha v_{n}$ L.I..

score 54 · Answer 15 · 2026-02-23 12:01:10

54

Views

Can you transpose a matrix before doing rref?

Published on 23 Feb 2026 - 12:01

List Question

Linear independence of $\begin{pmatrix}1\\ \vdots\\ \frac{1}{n}\end{pmatrix},\cdots,\begin{pmatrix}\frac{1}{n}\\ \vdots\\ \frac{1}{2n-1}\end{pmatrix}$

Prove: For full rank matrix $A\in\mathbb{C}^{m\times n}$ with $m>n$ and diagonal matrix $B\in\mathbb{C}^{n\times n}$ we have $rank(ABA^H)=n$

Gram Matrix and Linear Independence on Hilbert spaces source?

Contradiction between RREF & Determinant in evaluating Linear Independence

Find invertible matrices over a field such that the set of a vector multiplied by them is linearly independent

what is the quickest way of finding the set of all linearly independent sets over GF(2) and GF(3)?

Determine if a set of vectors is linearly independent or dependent?

What are some proofs that the list $1,z,...,z^m$ is linearly independent in $P(\mathbb{F})$ for each nonnegative integer $m$?

Linear independence of a matrix with only variables

Must linearly dependent vectors pass through the origin?

The $n\times n$ matrices $A^n, A^{n-1},\dots,\mathrm{id}_n$ are linearly dependent

How do we prove that $(x^4-6x^3), (x^3-6x^2), (x^2-6x)$, and $(x-6)$ are linearly independent?

If a vector in a linearly independent list is replaced by a linear combination of itself and one other vector is the result linearly independent?

$u_{1},...,u_{n}\in V$ L.I.. Then for any $v_{1},...,v_{n}\in V$, $\exists$ infinitely $\alpha$ s.t. $u_{1}+\alpha v_{1},...,u_{n}+\alpha v_{n}$ L.I..

Can you transpose a matrix before doing rref?

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