Skew-symmetric matrix, Principal minor, Diagonal similarity, Graph, Digraph, Orientation.
It is well known that two $n\times n$ symmetric matrices have equal corresponding principal minors of all orders if and only if they are diagonally similar. This result cannot be extended to arbitrary matrices. The aim of this work is to give a new transformation that preserves principal minors of skew-symmetric matrices.
BOUSSAIRI, Abderrahim and CHERGUI, Brahim.
"A transformation that preserves principal minors of skew-symmetric matrices",
Electronic Journal of Linear Algebra,
Volume 32, pp. 131-137.