# ON DOUBLY STOCHASTIC ${\kappa}-POTENT$ MATRICES AND REGULAR MATRICES

• Pyo, Sung-Soo (Department of Mathematics Education, Kyungpook National University)
• Published : 2000.05.01
• 41 3

#### 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

doubly stochastic;${\kappa}-potent$;regular elements

#### References

1. Inequalities : Theory of majorization and its applications A.W. Marshall;I. Olkin
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. Israel J. Math. v.15 Doubly stochastic matrix equations J.S. Montague;R.J. Plemmons
6. Linear and Multilin. Alg. v.21 The Theory of Permanents 1982-1985
7. Proc. Amer. Math. Soc. v.31 Generalized inverse of nonnegative matrices R.J. Plemmons;Cline
8. Mat. Casopis Sloven. Akad. Vied. v.17 A note on the structure of the semigroup of doubly stochastic matrices S. Schwarz
9. SIAM Nonnegative matrices in the mathematical sciences A. Berman;R.J. Plemmons
10. Linear and Multilin. Alg. v.12 The Theory of Permanents 1978-1981
11. Encyclopedia of Math. and Its Applics v.6 Permanents H. Minc