JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2015, Vol. 50 ›› Issue (02): 90-94.doi: 10.6040/j.issn.1671-9352.0.2014.227

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The minimal and maximal ranks problems of matrix expression A-BXC under generalized symmetric constraints

DAI Li-fang, LIANG Mao-lin, HE Wan-sheng   

  1. School of Mathematics and Statistics, Tianshui Normal University, Tianshui 741001, Gansu, China
  • Received:2014-05-16 Revised:2014-10-15 Online:2015-02-20 Published:2015-01-27

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Abstract: Let R,S be generalized reflection matrices, that is, R*=R, R2=I, S*=S, S2=I. A matrix X is called generalized reflective matrix (generalized skew-reflective matrix) if RXS=X(RXS=-X). The minimal and maximal ranks problems of matrix expression A-BXC with generalized reflective or skew-reflective matrices X are studied, and some solvability conditions of matrix equation BXC=A are derived.

Key words: generalized reflection matrices, generalized skew-reflective matrices, minimal and maximal ranks, matrix equations, generalized reflective matrices

CLC Number: 

  • O241.6
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