Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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THE EXTREMAL RANKS AND INERTIAS OF THE LEAST SQUARES SOLUTIONS TO MATRIX EQUATION AX = B SUBJECT TO HERMITIAN CONSTRAINT

  • Dai, Lifang (School of Mathematics and Statistics, Tianshui Normal University) ;
  • Liang, Maolin (School of Mathematics and Statistics, Tianshui Normal University)
  • Received : 2012.09.08
  • Accepted : 2012.10.07
  • Published : 2013.05.30
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Abstract

In this paper, the formulas for calculating the extremal ranks and inertias of the Hermitian least squares solutions to matrix equation AX = B are established. In particular, the necessary and sufficient conditions for the existences of the positive and nonnegative definite solutions to this matrix equation are given. Meanwhile, the least squares problem of the above matrix equation with Hermitian R-symmetric and R-skew symmetric constraints are also investigated.

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References

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