User Bach

2

votes

1

answer

1k

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the representation on the regular representation is faithful

Jul 18 '13 at 21:42 Andreas Blass 60k

21

votes

2

answers

7k

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Classsifying 1- and 2- dimensional Algebras, up to Isomorphism

differential-geometry lie-algebras

Jul 27 '15 at 0:06 muaddib 7,711

3

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1

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61

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$L=[LL]$ for classical algebras

lie-algebras

Aug 11 '13 at 5:53 Jared 29.2k

1

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1

answer

101

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For non-negative definite symmetric matrices, $\mathrm{tr}(AB)\le \mathrm{tr}(A)\mathrm{tr}(B)$ [duplicate]

matrices trace positive-semidefinite transpose matrix-norms

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Intuition behind row vectors of orthonormal matrix being an orthonormal basis

linear-algebra matrices vector-spaces

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28

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33k

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Column Vectors orthogonal implies Row Vectors also orthogonal?

linear-algebra matrices

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2

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653

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Subgroups of $\Bbb{R}^n$ that are closed and discrete

group-theory lie-groups lie-algebras abelian-groups

Jan 14 at 19:00 Bach 4,745

6

votes

1

answer

1k

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Discrete subgroups of $\mathbb R^n$ are free

linear-algebra abstract-algebra group-theory free-groups

Sep 21 '15 at 16:47 user26857 42.7k

1

vote

2

answers

130

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Suppose $G$ is a finite group. What can we say about the representations (matrices) corresponding to elements of $G$?

representation-theory

Jan 14 at 6:16 Bach 4,745

16

votes

3

answers

9k

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Symmetric and exterior power of representation

representation-theory

Mar 27 '19 at 18:14 Klaus 3,525

5

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2

answers

2k

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Dual space of exterior power and exterior power of dual space

linear-algebra multilinear-algebra exterior-algebra

Dec 28 '15 at 16:57 Community♦ 1

24

votes

2

answers

6k

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Exterior power “commutes” with direct sum

multilinear-algebra exterior-algebra

1d ago john 1,305

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1

answer

3k

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Distributivity of tensor products over direct sums for group representations

representation-theory tensor-products

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2

votes

1

answer

147

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Exterior algebra of polynomial ring with 2 variables

abstract-algebra exterior-algebra

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answers

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Ideals of a polynomial ring in infinitely many variables which are not finitely generated

abstract-algebra polynomials ring-theory ideals

Feb 29 '16 at 9:37 user26857 42.7k

11

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4

answers

2k

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$\hom(V,W)$ is canonic isomorph to $\hom(W^, V^)$

linear-algebra definition self-learning vector-space-isomorphism

Mar 2 '14 at 20:05 Community♦ 1

47

votes

1

answer

9k

views

Why is $\text{Hom}(V,W)$ the same thing as $V^* \otimes W$?

tensor-products

Feb 17 '14 at 16:57 Community♦ 1

13

votes

1

answer

2k

views

$U^*\otimes V$ versus $L(U,V)$ for infinite dimensional spaces

linear-algebra abstract-algebra tensor-products

Jun 11 '16 at 20:19 Community♦ 1

6

votes

1

answer

2k

views

Exterior power of dual space

linear-algebra

Jan 23 '11 at 15:50 Community♦ 1

4

votes

1

answer

146

views

Let $ R $ be a p.i.d. and $ A\in M_n(R) $. If $ \det(A)=1 $, prove or disprove that $ A $ can be expressed as products of elementary matrices.

abstract-algebra matrices principal-ideal-domains

Jan 25 '19 at 5:20 Bach 4,745

0

votes

1

answer

243

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Invertible matrix which can't be row reduced to $I$.

abstract-algebra matrices ring-theory

May 27 '17 at 22:05 user26857 42.7k

24

votes

4

answers

5k

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$(\mathbb{Q},+)$ has no maximal subgroups

abstract-algebra group-theory maximal-subgroup

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3

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1

answer

3k

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Subring of PID is also a PID?

abstract-algebra ring-theory

Nov 6 '16 at 7:54 Community♦ 1

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2

answers

3k

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Normal but not hermitian nor unitary

linear-algebra matrices

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1

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594

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Field of definition of representations of symmetric groups

representation-theory symmetric-groups

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Interpretation of the unsigned Stirling number of the first kind.

combinatorics stirling-numbers

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Stirling Numbers of the First Kind - a direct derivation

combinatorics generating-functions

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Stirling numbers of the first kind

combinatorics permutations stirling-numbers

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Prove that $\gcd(a^n - 1, a^m - 1) = a^{\gcd(n, m)} - 1$

elementary-number-theory divisibility faq gcd-and-lcm

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Product of all monic irreducibles with degree dividing $n$ in $\mathbb{F}_{q}$?

abstract-algebra polynomials finite-fields irreducible-polynomials

Dec 27 at 21:11 Bach 4,745

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the representation on the regular representation is faithful

Classsifying 1- and 2- dimensional Algebras, up to Isomorphism

$L=[LL]$ for classical algebras

For non-negative definite symmetric matrices, $\mathrm{tr}(AB)\le \mathrm{tr}(A)\mathrm{tr}(B)$ [duplicate]

Intuition behind row vectors of orthonormal matrix being an orthonormal basis

Column Vectors orthogonal implies Row Vectors also orthogonal?

Subgroups of $\Bbb{R}^n$ that are closed and discrete

Discrete subgroups of $\mathbb R^n$ are free

Suppose $G$ is a finite group. What can we say about the representations (matrices) corresponding to elements of $G$?

Symmetric and exterior power of representation

Dual space of exterior power and exterior power of dual space

Exterior power “commutes” with direct sum

Distributivity of tensor products over direct sums for group representations

Exterior algebra of polynomial ring with 2 variables

Ideals of a polynomial ring in infinitely many variables which are not finitely generated

$\hom(V,W)$ is canonic isomorph to $\hom(W^, V^)$

Why is $\text{Hom}(V,W)$ the same thing as $V^* \otimes W$?

$U^*\otimes V$ versus $L(U,V)$ for infinite dimensional spaces

Exterior power of dual space

Let $ R $ be a p.i.d. and $ A\in M_n(R) $. If $ \det(A)=1 $, prove or disprove that $ A $ can be expressed as products of elementary matrices.

Invertible matrix which can't be row reduced to $I$.

$(\mathbb{Q},+)$ has no maximal subgroups

Subring of PID is also a PID?

Normal but not hermitian nor unitary

Field of definition of representations of symmetric groups

Interpretation of the unsigned Stirling number of the first kind.

Stirling Numbers of the First Kind - a direct derivation

Stirling numbers of the first kind

Prove that $\gcd(a^n - 1, a^m - 1) = a^{\gcd(n, m)} - 1$

Product of all monic irreducibles with degree dividing $n$ in $\mathbb{F}_{q}$?