Question

Uncountable subset $X$ of $\mathbb{R^{n}}$ with property that every subset of $X$ with $n$ elements is a basis of $\mathbb{R}^{n}$.

score 71 · Answer 1 · 2022-01-18 17:25:00

71

Views

Uncountable subset $X$ of $\mathbb{R^{n}}$ with property that every subset of $X$ with $n$ elements is a basis of $\mathbb{R}^{n}$.

Published on 18 Jan 2022 - 17:25

score 35 · Answer 2 · 2022-01-30 10:06:18

35

Views

Linear Independence Condition

Published on 30 Jan 2022 - 10:06

score 118 · Answer 3 · 2022-01-30 14:44:53

118

Views

Basis for a column space

Published on 30 Jan 2022 - 14:44

score 103 · Answer 4 · 2022-02-04 07:11:13

103

Views

Any linear transformation there exists a basis such that $\phi(v_i) = \sum_{j=1}^n a_{ij} v_j$.

Published on 04 Feb 2022 - 7:11

score 61 · Answer 5 · 2022-02-12 22:25:30

61

Views

Computability of Vector Representations without Inner Products.

Published on 12 Feb 2022 - 22:25

score 78 · Answer 6 · 2022-02-15 12:56:18

78

Views

Difficulty understanding the link between the span of a sequence being an isomorph of $\ell_1$ and that sequence being a basis of the closed span

Published on 15 Feb 2022 - 12:56

score 206 · Answer 7 · 2022-02-21 22:37:29

206

Views

If $S$ is a spanning set of a vector space, must there be a subset of $S$ which is a basis?

Published on 21 Feb 2022 - 22:37

score 57 · Answer 8 · 2022-03-21 09:44:10

57

Views

Give a example to show that there not necessarily exist $\{e_j\}$ such that $f_i(e_j)=\delta_{ij}, i,j\geq 1$.

Published on 21 Mar 2022 - 9:44

score 51 · Answer 9 · 2022-04-08 16:36:19

51

Views

Given a basis $X$ for a finite dimentional vector space $V$, prove that $L(X)$ spans $L(V)$.

Published on 08 Apr 2022 - 16:36

score 80 · Answer 10 · 2022-04-16 08:36:52

80

Views

Prove that the algebraic dimension of an infinite dimensional Banach space is atleast $\mathfrak{c}$.

Published on 16 Apr 2022 - 8:36

score 75 · Answer 11 · 2022-05-08 14:14:48

75

Views

What is an example of spanning set with linearly independent vectors that is not a Hamel Basis?

Published on 08 May 2022 - 14:14

score 97 · Answer 12 · 2022-05-18 09:01:41

97

Views

Total orthonormal set which is not a basis

Published on 18 May 2022 - 9:01

score 35 · Answer 13 · 2022-05-28 09:28:40

35

Views

Where I went wrong in this chain of arguments - Linear algebra

Published on 28 May 2022 - 9:28

score 409 · Answer 14 · 2022-06-03 04:05:19

409

Views

Relation of Hamel basis with the equation $f(x + y) = f(x) + f(y)$?

Published on 03 Jun 2022 - 4:05

score 340 · Answer 15 · 2022-07-08 04:15:40

340

Views

Understanding the proof of "If $V$ is $n$ dimensional vectors space then a set in $V$ with fewer than $n$ vectors does not span $V$ "

Published on 08 Jul 2022 - 4:15

List Question

Uncountable subset $X$ of $\mathbb{R^{n}}$ with property that every subset of $X$ with $n$ elements is a basis of $\mathbb{R}^{n}$.

Linear Independence Condition

Basis for a column space

Any linear transformation there exists a basis such that $\phi(v_i) = \sum_{j=1}^n a_{ij} v_j$.

Computability of Vector Representations without Inner Products.

Difficulty understanding the link between the span of a sequence being an isomorph of $\ell_1$ and that sequence being a basis of the closed span

If $S$ is a spanning set of a vector space, must there be a subset of $S$ which is a basis?

Give a example to show that there not necessarily exist $\{e_j\}$ such that $f_i(e_j)=\delta_{ij}, i,j\geq 1$.

Given a basis $X$ for a finite dimentional vector space $V$, prove that $L(X)$ spans $L(V)$.

Prove that the algebraic dimension of an infinite dimensional Banach space is atleast $\mathfrak{c}$.

What is an example of spanning set with linearly independent vectors that is not a Hamel Basis?

Total orthonormal set which is not a basis

Where I went wrong in this chain of arguments - Linear algebra

Relation of Hamel basis with the equation $f(x + y) = f(x) + f(y)$?

Understanding the proof of "If $V$ is $n$ dimensional vectors space then a set in $V$ with fewer than $n$ vectors does not span $V$ "

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