Question

If $\zeta_n$ is the $nth$ root of unity, find $\dim_{\Bbb Q}\Bbb Q[\zeta_n]$

score 265 · Answer 1 · 2026-03-26 06:31:52

265

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If $\zeta_n$ is the $nth$ root of unity, find $\dim_{\Bbb Q}\Bbb Q[\zeta_n]$

Published on 26 Mar 2026 - 6:31

score 195 · Answer 2 · 2026-03-26 04:53:38

195

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If $\zeta_n$ is a primitive $n$th root of unity, why is $\text{dim}_{\Bbb Q}\Bbb Q[\zeta_n]=\phi(n)$?

Published on 26 Mar 2026 - 4:53

score 59 · Answer 3 · 2018-08-16 13:10:55

59

Views

What is $W_1 + W_2$ if $W_1\subset W_2$?

Published on 16 Aug 2018 - 13:10

score 106 · Answer 4 · 2026-03-29 22:33:16

106

Views

Find the Dimension of the Centraliser of Matrix $A$

Published on 29 Mar 2026 - 22:33

score 1.1k · Answer 5 · 2018-08-17 05:01:23

Show that a infinite dimensional vector space must have linearly independent vectors for every positive integer

score 723 · Answer 6 · 2026-03-30 01:29:42

723

Views

Proving $\mid \parallel x \parallel - \parallel y \parallel \mid$ $\leqq$ $\parallel x-y \parallel$?

Published on 30 Mar 2026 - 1:29

score 64 · Answer 7 · 2018-08-17 12:37:51

64

Views

Confusion regarding transformation matrix

Published on 17 Aug 2018 - 12:37

score 115 · Answer 8 · 2026-03-25 15:46:12

115

Views

How do I decompose a vector into $2$ orthogonal vectors where all coordinates are integers?

Published on 25 Mar 2026 - 15:46

score 310 · Answer 9 · 2018-08-17 22:13:31

310

Views

Extending inner product from subspace to whole space

Published on 17 Aug 2018 - 22:13

score 55 · Answer 10 · 2018-08-18 12:31:06

55

Views

Linear dependence over the null field

Published on 18 Aug 2018 - 12:31

score 1.1k · Answer 11 · 2018-08-18 13:46:16

1.1k

Views

Showing that set of all vectors orthogonal to two vectors is a subspace.

Published on 18 Aug 2018 - 13:46

score 82 · Answer 12 · 2026-03-26 07:33:33

82

Views

Definition of orthogonal subspace

Published on 26 Mar 2026 - 7:33

score 1k · Answer 13 · 2018-08-18 17:03:57

Prove that if $W$ is a subspace of $V$ vector space, and $(V\setminus W) \cup \{ 0\ $} is also a subspace of $V$, then $W=V$ or $W=\{0\}$

score 678 · Answer 14 · 2026-03-26 07:38:25

678

Views

Orthogonal complements in arbitrary normed spaces

Published on 26 Mar 2026 - 7:38

score 197 · Answer 15 · 2018-08-20 10:15:04

197

Views

Finding matrices which P is null space

Published on 20 Aug 2018 - 10:15

List Question

If $\zeta_n$ is the $nth$ root of unity, find $\dim_{\Bbb Q}\Bbb Q[\zeta_n]$

If $\zeta_n$ is a primitive $n$th root of unity, why is $\text{dim}_{\Bbb Q}\Bbb Q[\zeta_n]=\phi(n)$?

What is $W_1 + W_2$ if $W_1\subset W_2$?

Find the Dimension of the Centraliser of Matrix $A$

Show that a infinite dimensional vector space must have linearly independent vectors for every positive integer

Proving $\mid \parallel x \parallel - \parallel y \parallel \mid$ $\leqq$ $\parallel x-y \parallel$?

Confusion regarding transformation matrix

How do I decompose a vector into $2$ orthogonal vectors where all coordinates are integers?

Extending inner product from subspace to whole space

Linear dependence over the null field

Showing that set of all vectors orthogonal to two vectors is a subspace.

Definition of orthogonal subspace

Prove that if $W$ is a subspace of $V$ vector space, and $(V\setminus W) \cup \{ 0\ $} is also a subspace of $V$, then $W=V$ or $W=\{0\}$

Orthogonal complements in arbitrary normed spaces

Finding matrices which P is null space

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