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Information Journal Paper

Title

INVESTIGATION ON THE HERMITIAN MATRIX EXPRESSION SUBJECT TO SOME CONSISTENT EQUATIONS

Pages

  9-28

Abstract

 In this paper, we study the extremal ranks and inertias of the Hermitian matrix expressionf (X, Y) =C4-B4Y- (B4Y)*-A4XA*4’where C4 is Hermitian, *denotes the conjugate transpose, X and Y satisfy the following consistent system of matrix equations A3Y= C3, A1X=C1, XB1=D1, A2XA*2=C2, X=X*. As consequences, we get the necessary and sufficient conditions for the above expression f (X; Y) to be (semi) positive, (semi) negative. The relations between the Hermitian part of the solution to the matrix equation A3Y=C3 and the Hermitian solution to the system of matrix equations A1X=C1, XB1=D1, A2XA*2=C2 are also characterized. Moreover, we give the necessary and sufficient conditions for the solvability to the following system of matrix equations A3Y=C3, A1X=C1, XB1=D1, A2XA*2=C2, X=X*, B4Y+ (B4Y) *+A4XA*4=C4 and provide an expression of the general solution to this system when it is solvable.

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    • Cite

    APA: Copy

    ZHANG, XIANG. (2014). INVESTIGATION ON THE HERMITIAN MATRIX EXPRESSION SUBJECT TO SOME CONSISTENT EQUATIONS. BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, 40(1), 9-28. SID. https://sid.ir/paper/618011/en

    Vancouver: Copy

    ZHANG XIANG. INVESTIGATION ON THE HERMITIAN MATRIX EXPRESSION SUBJECT TO SOME CONSISTENT EQUATIONS. BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY[Internet]. 2014;40(1):9-28. Available from: https://sid.ir/paper/618011/en

    IEEE: Copy

    XIANG ZHANG, “INVESTIGATION ON THE HERMITIAN MATRIX EXPRESSION SUBJECT TO SOME CONSISTENT EQUATIONS,” BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, vol. 40, no. 1, pp. 9–28, 2014, [Online]. Available: https://sid.ir/paper/618011/en

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