J4 ›› 2013, Vol. 48 ›› Issue (10): 47-50.

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The solvable condition researched on a pair of matrix equations

JIANG Jing1, LI Ning2, WANG Ting1   

  1. 1.Department of Mathematics, Qilu Normal University, Jinan 250013, Shandong, China;
    2. School of Statistics and Mathematics, Shandong Finance University, Jinan 250014, Shandong, China
  • Received:2012-12-19 Published:2013-10-14

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Abstract:

The matrix equations A1XA*1+B1YB*1=C1
A2XA*2+B2YB*2=C2 are studied, where Ci=C*i, i=1, 2. By the rank of matrix, a necessary and sufficient condition is given for the matrix equations to have a pair of common Hermitian solutions X and Y. As a consequence, we have derived the conditions for the matrix equations to have Hermitian solution X or Y respectively by ranks.

Key words: matrix equations; Hermitian solution; minimal rank; maximal rank

CLC Number: 

  • O151
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