On the similarity of matrices $AB$ and $BA$ over a field
On the similarity of matrices $AB$ and $BA$ over a field
Let $A$ and $B$ be $n$-by-$n$ matrices over a field. The study of the relationship between the products of matrices $AB$ and $BA$ has a long history. It is well-known that $AB$ and $BA$ have equal characteristic polynomials (and, therefore, eigenvalues, traces, etc.). One beautiful result was obtained by H. …