Linear operators that preserve spanning column ranks of nonnegative matrices

  • Hwang, Suk-Geun (Department of Mathematics Education Teachers College, Kyungpook University) ;
  • Kim, Si-Ju (Department of Mathematics Education Andong University) ;
  • Song, Seok-Zun (Department of Mathematics Cheju National University)
  • 발행 : 1994.11.01

초록

If S is a semiring of nonnegative reals, which linear operators T on the space of $m \times n$ matrices over S preserve the column rank of each matrix\ulcorner Evidently if P and Q are invertible matrices whose inverses have entries in S, then $T : X \longrightarrow PXQ$ is a column rank preserving, linear operator. Beasley and Song obtained some characterizations of column rank preserving linear operators on the space of $m \times n$ matrices over $Z_+$, the semiring of nonnegative integers in [1] and over the binary Boolean algebra in [7] and [8]. In [4], Beasley, Gregory and Pullman obtained characterizations of semiring rank-1 matrices and semiring rank preserving operators over certain semirings of the nonnegative reals. We considers over certain semirings of the nonnegative reals. We consider some results in [4] in view of a certain column rank instead of semiring rank.

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