Question

If vectors in a set is linearly independent to each other, does it make the set an linearly independent set? Why or why not?

score 41 · Answer 1 · 2022-09-14 10:01:56

41

Views

If vectors in a set is linearly independent to each other, does it make the set an linearly independent set? Why or why not?

Published on 14 Sep 2022 - 10:01

score 60 · Answer 2 · 2022-09-14 12:39:05

60

Views

If $\theta$ is linearly indep. to $\pi,$ then is $\liminf_{n\to\infty}f(n)\left\vert\cos(n\theta)\right\vert=+\infty$ where $f(n)=n^k?$ or $f(n)=2^n?$

Published on 14 Sep 2022 - 12:39

score 80 · Answer 3 · 2022-09-18 16:40:26

80

Views

How are these two theorems about linear independence equivalent/saying the same thing?

Published on 18 Sep 2022 - 16:40

score 68 · Answer 4 · 2022-09-22 18:39:37

68

Views

Why is it the case that when the columns of a matrix are dependent, then the rows of the matrix are dependent also?

Published on 22 Sep 2022 - 18:39

score 95 · Answer 5 · 2022-09-25 23:18:34

95

Views

Let $S,L\subset V$, both finite. If $\textrm{span}(S)=V$ and $L$ is LI, $|S| \geq |L|$. (Artin's proof and alternative proof.)

Published on 25 Sep 2022 - 23:18

score 109 · Answer 6 · 2022-09-26 05:10:51

109

Views

Prove that $f(x) = x^3$ and $g(x) = x^2|x|$ are not linearly dependant on the interval $[-1, 1]$

Published on 26 Sep 2022 - 5:10

score 65 · Answer 7 · 2022-10-04 18:16:19

65

Views

Let $V$ be a $K$-vector space of dimension $n \ge1$ and let $B \subset V$ . At following statements are equivalent:

Published on 04 Oct 2022 - 18:16

score 102 · Answer 8 · 2022-10-05 00:44:35

102

Views

Proof that monomials of $\mathbb{P}_n(x)$ are linearly independent

Published on 05 Oct 2022 - 0:44

score 349 · Answer 9 · 2022-10-07 02:33:07

349

Views

I showed that $AX = b_1$ has a unique solution. Does it mean that the columns of $A$ are linearly independent?

Published on 07 Oct 2022 - 2:33

score 92 · Answer 10 · 2022-10-11 20:27:38

92

Views

Quickly determine if vectors are independent

Published on 11 Oct 2022 - 20:27

score 175 · Answer 11 · 2022-10-15 05:33:01

175

Views

Generalizing the entries of a (3x3) symmetric matrix and calculating the projection onto its range

Published on 15 Oct 2022 - 5:33

score 68 · Answer 12 · 2022-10-15 20:53:42

68

Views

Linear Dependence and Linear Independence Equation . I don't really understand the formula.

Published on 15 Oct 2022 - 20:53

score 119 · Answer 13 · 2022-10-16 07:24:32

119

Views

If $T^rv=v$, are $v,Tv,\ldots,T^{r-1}v$ linearly independent?

Published on 16 Oct 2022 - 7:24

score 97 · Answer 14 · 2022-10-18 21:51:40

97

Views

True or False: A set $(u,v,w)$ of vector is linearly independent if $u$ is not a linear combination of $v$ and $w$.

Published on 18 Oct 2022 - 21:51

score 96 · Answer 15 · 2022-10-21 07:19:21

96

Views

When will "permuted vectors" be linearly independent?

Published on 21 Oct 2022 - 7:19

List Question

If vectors in a set is linearly independent to each other, does it make the set an linearly independent set? Why or why not?

If $\theta$ is linearly indep. to $\pi,$ then is $\liminf_{n\to\infty}f(n)\left\vert\cos(n\theta)\right\vert=+\infty$ where $f(n)=n^k?$ or $f(n)=2^n?$

How are these two theorems about linear independence equivalent/saying the same thing?

Why is it the case that when the columns of a matrix are dependent, then the rows of the matrix are dependent also?

Let $S,L\subset V$, both finite. If $\textrm{span}(S)=V$ and $L$ is LI, $|S| \geq |L|$. (Artin's proof and alternative proof.)

Prove that $f(x) = x^3$ and $g(x) = x^2|x|$ are not linearly dependant on the interval $[-1, 1]$

Let $V$ be a $K$-vector space of dimension $n \ge1$ and let $B \subset V$ . At following statements are equivalent:

Proof that monomials of $\mathbb{P}_n(x)$ are linearly independent

I showed that $AX = b_1$ has a unique solution. Does it mean that the columns of $A$ are linearly independent?

Quickly determine if vectors are independent

Generalizing the entries of a (3x3) symmetric matrix and calculating the projection onto its range

Linear Dependence and Linear Independence Equation . I don't really understand the formula.

If $T^rv=v$, are $v,Tv,\ldots,T^{r-1}v$ linearly independent?

True or False: A set $(u,v,w)$ of vector is linearly independent if $u$ is not a linear combination of $v$ and $w$.

When will "permuted vectors" be linearly independent?

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