Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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ON DOUBLY STOCHASTIC ${\kappa}-POTENT$ MATRICES AND REGULAR MATRICES

  • Pyo, Sung-Soo (Department of Mathematics Education, Kyungpook National University)
  • Published : 2000.05.01
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Abstract

In this paper, we determine the structure of ${\kappa}-potent$ elements and regular elements of the semigroup ${\Omega}_n$of doubly stochastic matrices of order n. In connection with this, we find the structure of the matrices X satisfying the equation AXA = A. From these, we determine a condition of a doubly stochastic matrix A whose Moore-Penrose generalized is also a doubly stochastic matrix.

Keywords

References

  1. SIAM Nonnegative matrices in the mathematical sciences A. Berman;R.J. Plemmons
  2. Trans. Amer. Math. Soc. v.52 Topics in the theory of Markov chains J.L. Doob
  3. Proc. Glasgow Math. Assoc. v.7 The semigroup of doubly stochastic matrices H.K. Farahat
  4. Merrill Research and Lecture Series. Columbus Ohio. Elements of compact semigroups K.H. Hoffman;P.S. Mostert
  5. Inequalities : Theory of majorization and its applications A.W. Marshall;I. Olkin
  6. Encyclopedia of Math. and Its Applics v.6 Permanents H. Minc
  7. Linear and Multilin. Alg. v.12 The Theory of Permanents 1978-1981
  8. Linear and Multilin. Alg. v.21 The Theory of Permanents 1982-1985
  9. Israel J. Math. v.15 Doubly stochastic matrix equations J.S. Montague;R.J. Plemmons
  10. Proc. Amer. Math. Soc. v.31 Generalized inverse of nonnegative matrices R.J. Plemmons;Cline
  11. Mat. Casopis Sloven. Akad. Vied. v.17 A note on the structure of the semigroup of doubly stochastic matrices S. Schwarz