Further properties of the star, left-star, right-star, and minus partial orderings
J. K. Baksalary1 , O. M. Baksalary2 , X. Liu3,4
1 Institute of Mathematics, Zielona Góra University, ul. Podgórna 50, PL 65-246, Zielona Góra, Poland
2 Institute of Physics, Adam Mickiewicz University, ul. Umultowska 85, PL 61-614, Poznań , Poland
3 Department of Applied Mathematics, Xidian University, Xian 710071, People’s Republic of China
4 Department of Mathematics, Suzhou Railway Teacher’s College, Suzhou 215009, People’s Republic of China
Linear Algebra and its Applications, 375, 83-94 (2003)
Certain classes of matrices are indicated for which the star, left-star, right-star, and minus partial orderings, or some of them, are equivalent. Characterizations of the left-star and right-star orderings, similar to those devised by Hartwig and Styan [Linear Algebra Appl. 82 (1986) 145] for the star and minus orderings, are established along with other auxiliary results, which are of independent interest as well. Some inheritance-type properties of matrices are also given. The class of EP matrices appears to be essential in several points of our considerations.