User Cayley-Hamilton

9 votes

Is there a simpler, more abstract proof of the Cayley-Hamilton theorem for matrices?

answered Apr 24, 2019 at 16:45

5 votes

Accepted

On Mazur-Ulam theorem

answered Mar 26, 2017 at 16:42

5 votes

Accepted

Direct sum of Prüfer groups and $\mathbb Q/\mathbb Z$

answered Feb 26, 2017 at 23:41

4 votes

Accepted

Isomorphism of Hom sets

answered Mar 8, 2017 at 1:09

4 votes

Intuitive way of thinking about quotient topology

answered Apr 21, 2018 at 1:37

4 votes

Accepted

Is $\operatorname{Hom}(A\oplus B, C)=\operatorname{Hom}(A,C)\oplus\operatorname{Hom}(B,C)$? Where can I find general rules for $\operatorname{Hom}$?

answered Aug 30, 2021 at 15:15

3 votes

Accepted

Looking for Abstract Proofs of Nakayama Lemma/Hamilton-Cayley Theorem

answered Apr 23, 2019 at 23:07

3 votes

What is the concept for a category created by exchanging the roles of objects and morphisms in another category?

answered Jul 17, 2019 at 14:21

3 votes

Equality in Cauchy-Schwarz

answered Oct 8, 2019 at 3:35

3 votes

Accepted

why splitting lemma fails for nonabelian groups?

answered Feb 28, 2019 at 21:07

3 votes

Short exact sequence of algebras implies bimodule structure

answered Apr 17, 2019 at 21:34

3 votes

Accepted

If M is finitely generated module, then it has finite rank.

answered Mar 2, 2017 at 0:58

3 votes

The dimension of the kernel of $X \to AX-XA$ is the sum of the squares of the multiplicities of the eigenvalues of $A$

answered Mar 24, 2017 at 19:30

2 votes

Accepted

What is the value of the $X$?

answered Mar 12, 2017 at 19:08

2 votes

Explain how to obtain a field with $125$ elements using polynomials by using concrete example provided by a polynomial

answered Mar 24, 2017 at 23:49

2 votes

If union of n subspaces of V is a subspace of V, then one of the n subspaces must contain the other n-1 subspaces

answered Jan 21, 2019 at 4:25

2 votes

Accepted

Relation between $\|\operatorname{proj}_P(u)\|$ and $\|u \times v\|$ where $v$ is the normal to $P$

answered Mar 24, 2017 at 21:35

2 votes

Topology in Infinite Galois Theory.

answered Apr 15, 2019 at 22:57

2 votes

Prove that any $R$-module $M$ is isomorphic to $\mathrm{hom}_R(R,M)$

answered Apr 23, 2019 at 22:27

2 votes

Accepted

Finite abelian group generated by two elements

answered Apr 21, 2018 at 20:20

2 votes

Accepted

Show that matrix of $T$ has at least dim range $T$ nonzero entries.

answered Mar 1, 2019 at 0:24

2 votes

Cayley Hamilton Theorem Intuition

answered Apr 23, 2019 at 23:04

2 votes

Accepted

The number of pairs $(A,B)$ of subsets of a set $X$

answered Apr 28, 2019 at 18:34

1 vote

Accepted

Splitting field of $\sqrt{\vphantom{\sum}1+{\sqrt2}}$ and Galois group

answered Apr 15, 2019 at 18:45

1 vote

Intersection of finite Galois extensions is Galois

answered Apr 15, 2019 at 22:36

1 vote

Accepted

For $p(x)$ and $q(x)$ in $\overline{\mathbb{Q}}[x]$, if $p(x)$ is coprime to $q(x)$, and $m\leq n$, then is $p(x)^n$ coprime to $q(x)^m$?

answered Jan 12, 2020 at 22:58

1 vote

Decomposing vector space into direct sums

answered Sep 22, 2020 at 1:37

1 vote

Annihilator of a module homomorphism

answered Aug 1 at 18:42

1 vote

Accepted

Questions on the proof of Cayley Hamilton Theorem

answered Apr 25, 2019 at 16:33

1 vote

Accepted

Category of G-equivariant sets

answered Mar 3, 2019 at 0:24

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72 Answers

Is there a simpler, more abstract proof of the Cayley-Hamilton theorem for matrices?

On Mazur-Ulam theorem

Direct sum of Prüfer groups and $\mathbb Q/\mathbb Z$

Isomorphism of Hom sets

Intuitive way of thinking about quotient topology

Is $\operatorname{Hom}(A\oplus B, C)=\operatorname{Hom}(A,C)\oplus\operatorname{Hom}(B,C)$? Where can I find general rules for $\operatorname{Hom}$?

Looking for Abstract Proofs of Nakayama Lemma/Hamilton-Cayley Theorem

What is the concept for a category created by exchanging the roles of objects and morphisms in another category?

Equality in Cauchy-Schwarz

why splitting lemma fails for nonabelian groups?

Short exact sequence of algebras implies bimodule structure

If M is finitely generated module, then it has finite rank.

The dimension of the kernel of $X \to AX-XA$ is the sum of the squares of the multiplicities of the eigenvalues of $A$

What is the value of the $X$?

Explain how to obtain a field with $125$ elements using polynomials by using concrete example provided by a polynomial

If union of n subspaces of V is a subspace of V, then one of the n subspaces must contain the other n-1 subspaces

Relation between $\|\operatorname{proj}_P(u)\|$ and $\|u \times v\|$ where $v$ is the normal to $P$

Topology in Infinite Galois Theory.

Prove that any $R$-module $M$ is isomorphic to $\mathrm{hom}_R(R,M)$

Finite abelian group generated by two elements

Show that matrix of $T$ has at least dim range $T$ nonzero entries.

Cayley Hamilton Theorem Intuition

The number of pairs $(A,B)$ of subsets of a set $X$

Splitting field of $\sqrt{\vphantom{\sum}1+{\sqrt2}}$ and Galois group

Intersection of finite Galois extensions is Galois

For $p(x)$ and $q(x)$ in $\overline{\mathbb{Q}}[x]$, if $p(x)$ is coprime to $q(x)$, and $m\leq n$, then is $p(x)^n$ coprime to $q(x)^m$?

Decomposing vector space into direct sums

Annihilator of a module homomorphism

Questions on the proof of Cayley Hamilton Theorem

Category of G-equivariant sets