All Questions
3
questions
7
votes
3
answers
399
views
Smallest faithful representation of an upper-triangular matrix quotient
This is a curiosity question that came out of teaching abstract algebra.
Let $F$ be a field, and $n>1$ an integer.
Let $F^{n \leq n}$ be the $F$-algebra of all upper-triangular $n\times n$-matrices ...
- 32.7k
1
vote
0
answers
63
views
"embedding" various matrix equivalences into the equivalence of particular linear map
Consider the square matrices over a (local) ring $R$, up to conjugation, $A\rightarrow UAU^{-1}$, where $U$ is an invertible matrix over $R$. Such an equivalence embeds into the "left-right" ...
- 2,202
0
votes
0
answers
49
views
Rank of Coxeter matrix
Let $Q$ be a quiver and $\Phi_Q$ be the Coxeter matrix of $Q$.
Then $\Phi_Q\pm I$ are full-rank?
- 489