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 61 · Answer 1 · 2023-08-06 04:04:12

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 75 · Answer 2 · 2023-08-11 18:53:28

75

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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 11 Aug 2023 - 18:53

score 53 · Answer 3 · 2023-08-17 10:15:23

53

Views

Gram Matrix and Linear Independence on Hilbert spaces source?

Published on 17 Aug 2023 - 10:15

score 34 · Answer 4 · 2023-08-27 02:05:01

34

Views

Contradiction between RREF & Determinant in evaluating Linear Independence

Published on 27 Aug 2023 - 2:05

score 94 · Answer 5 · 2023-09-04 20:52:33

94

Views

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

Published on 04 Sep 2023 - 20:52

score 44 · Answer 6 · 2023-09-05 22:21:13

44

Views

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

Published on 05 Sep 2023 - 22:21

score 83 · Answer 7 · 2023-09-08 00:08:42

83

Views

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

Published on 08 Sep 2023 - 0:08

score 94 · Answer 8 · 2023-09-10 12:29:11

94

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 10 Sep 2023 - 12:29

score 39 · Answer 9 · 2023-10-01 11:39:21

39

Views

Linear independence of a matrix with only variables

Published on 01 Oct 2023 - 11:39

score 105 · Answer 10 · 2023-10-02 06:33:01

105

Views

Must linearly dependent vectors pass through the origin?

Published on 02 Oct 2023 - 6:33

score 167 · Answer 11 · 2023-10-02 20:41:17

167

Views

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

Published on 02 Oct 2023 - 20:41

score 97 · Answer 12 · 2023-10-06 07:24:01

97

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 06 Oct 2023 - 7:24

score 163 · Answer 13 · 2023-10-09 01:05:08

163

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 09 Oct 2023 - 1:05

score 71 · Answer 14 · 2023-10-21 06:41:10

$u_{1},...,u_{n}\in V$ 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 53 · Answer 15 · 2023-10-24 00:33:37

53

Views

Can you transpose a matrix before doing rref?

Published on 24 Oct 2023 - 0:33

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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