A transformation that preserves principal minors of skew-symmetric\n matrices

2016/06/29 by Abderrahim Boussaïri, Boussaïri, Abderrahim, Brahim Chergui +1
Computer Science · Engineering · #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Matrix Theory and Algorithms #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1606.09081

openalex publication_date 2016/06/29 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

Our motivation comes from the work of Engel and Schneider (1980). Their main\ntheorem implies that two symmetric matrices have equal corresponding principal\nminors of all orders if and only if they are diagonally similar. This study was\ncontinued by Hartfiel and Loewy (1984). They found sufficient conditions under\nwhich two n\× n matrices A and B have equal corresponding principal\nminors of all orders if and only if B or its transpose B^t is diagonally\nsimilar to A. In this paper, we give a new way to construct a pair of\nskew-symmetric having equal corresponding principal minors of all orders.\n

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