$G$-circulant Matrices and the Classical Maschke Theorem
In this note, we use the isomorphism of the ring of $G$-circulant matrices over a field $k$ with the group ring $k[G]$ to derive a very short proof of the Classical Maschke Theorem.
math.RT↗
arXiv subjects
Jon Merzel
Publications and source records attributed to Jon Merzel.
Spectral perturbation by rank one matrices
Let $A$ be a matrix of size $n \times n$ over an algebraically closed field $F$ and $q(t)$ a monic polynomial of degree $n$. In this article, we describe the necessary and sufficient conditions of $q(t)$ so that there exists a rank one matrix $B$ such that the characteristic polynomial of $A+B$ is $q(t)$.
math.SP↗