SOME FURTHER NOTES ON THE MATRIX EQUATIONS ATXB + BTXTA = C ANDATXB + BTXA = C

doi:10.1016/S0252-9602(14)60156-9

Acta mathematica scientia,Series B ›› 2015, Vol. 35 ›› Issue (1): 275-280.doi: 10.1016/S0252-9602(14)60156-9

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SOME FURTHER NOTES ON THE MATRIX EQUATIONS A^TXB + B^TX^TA = C ANDA^TXB + B^TXA = C

G.SOARES

Center of Mathematics, University of Tr´as-os-Montes of Alto Douro, Apartado 1013, 5001-801 Vila Real, Portugal

Received:2013-11-06 Revised:2014-02-21 Online:2015-01-20 Published:2015-01-20
Supported by:
This work was partially supported by FCT (Portugal) with national funds through Centro de Matem´atica da Universidade de Tr´as-os-Montes e Alto Douro (PEst-OE/MAT/UI4080/2014).

Abstract

Abstract:

Dehghan and Hajarian, [4], investigated the matrix equations ATXB+BTXTA = C and ATXB + BTXA = C providing inequalities for the determinant of the solutions of these equations. In the same paper, the authors presented a lower bound for the product of the eigenvalues of the solutions to these matrix equations. Inspired by their work, we give some generalizations of Dehghan and Hajarian results. Using the theory of the numerical ranges, we present an inequality involving the trace of C when A,B,X are normal matrices satisfying ATB = BAT

Key words: matrix equation, eigenvalue, trace, permutation matrix

CLC Number:

15A24

G.SOARES. SOME FURTHER NOTES ON THE MATRIX EQUATIONS A^TXB + B^TX^TA = C ANDA^TXB + B^TXA = C[J].Acta mathematica scientia,Series B, 2015, 35(1): 275-280.

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SOME FURTHER NOTES ON THE MATRIX EQUATIONS A^TXB + B^TX^TA = C ANDA^TXB + B^TXA = C

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