Similarity for zero-square matrices
Rings and Algebras
2022-02-18 v4
Abstract
Let T be an n by n zero-square matrix over a commutative unital ring R. We show that T is similar to a multiple of E_1n if R is a GCD domain and n = 2, if R is a GCD domain with 2 not zero divisor and n = 3, but there are matrices which are not similar to any multiple of E_1n whenever n greater or equal 4, over any commutative unital ring.
Keywords
Cite
@article{arxiv.2108.12882,
title = {Similarity for zero-square matrices},
author = {Grigore Calugareanu},
journal= {arXiv preprint arXiv:2108.12882},
year = {2022}
}