J4 ›› 2010, Vol. 45 ›› Issue (4): 106-110.

• Articles • Previous Articles    

Extremal ranks for block Hermitian and skew-Hermitian matrices

ZHANG Feng-xia1, LI Ying1,2, GUO Wen-bin1,  ZHAO Jian-li1   

  1. 1. College of Mathematics Science, Liaocheng University, Liaocheng 252059, Shandong, China;
    2. School of Management, University of Shanghai for Science and Technology, Shanghai 200093, China
  • Received:2009-09-09 Online:2010-04-10 Published:2010-05-19

Abstract:

In this paper, by using the ranks of several expressions about Hermitian matrices and skew-Hermitian matrices and the characters of block matrices, the maximal ranks and minimal ranks of the block Hermitian {AB*BX} with respect to X are investigated, where X is an arbitrary Hermitian matrices or X is the Hermitian solutions to the matrix equation BXB*=A(A=A*). And the maximal ranks and minimal ranks of the block skewHermitian matrix {A-B*BX}with respect to X are investigated, where X is an arbitrary skew-Hermitian matrix or X is the skew-Hermitian solutions to the matrix equation BXB*=A(A=-A*).

Key words: block Hermite matrices; block skew-Hermite matrices; maximal rank; minimal rank

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