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The -Reflexive Solution to System of Matrix Equations

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  • Chang-Zhou Dong
  • Qing-Wen Wang

Abstract

Let and be Hermitian and -potent matrices; that is, and where stands for the conjugate transpose of a matrix. A matrix is called -reflexive (antireflexive) if . In this paper, the system of matrix equations and subject to -reflexive and antireflexive constraints is studied by converting into two simpler cases: and We give the solvability conditions and the general solution to this system; in addition, the least squares solution is derived; finally, the associated optimal approximation problem for a given matrix is considered.

Suggested Citation

  • Chang-Zhou Dong & Qing-Wen Wang, 2015. "The -Reflexive Solution to System of Matrix Equations ," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-9, November.
    • Handle: RePEc:hin:jnlmpe:464385
    DOI: 10.1155/2015/464385
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