A matrix A is said to be matrix majorized by a matrix B, written A ≺ B, if there exists an n× n row stochastic matrix X such that A = BX. This is a generalization of multivariate majorization. In… (More)

Let A and B be m n matrices. A linear operator T preserves the set of matrices on which the rank is additive if rank(A + B) = rank(A) + rank(B) implies that rank(T (A) + T(B)) = rankT (A) + rankT… (More)

Let A be a (0, 1, ∗)-matrix with main diagonal all 0’s and such that if ai,j = 1 or ∗ then aj,i = ∗ or 0. Underwhat conditions on the row sums, and or column sums, of A is it possible to change the… (More)

Let A be a Boolean {0, 1} matrix. The isolation number of A is the maximum number of ones in A such that no two are in any row or any column (that is they are independent), and no two are in a 2 × 2… (More)

Beasley, L.B. and N.J. Pullman, Linear operators that strongly preserve graphical properties of matrices, Discrete Mathematics 104 (1992) 143-157. An operator on the set Ju of n X n matrices strongly… (More)

In this paper, a covariance matrix of circulant correlation, R, is studied. A pattern of entries in R−1 independent of the value ρ of the correlation coefficient is proved based on a recursive… (More)

We obtain characterizations of Boolean linear operators that preserve some of the isolation numbers of Boolean matrices. In particular, we show that the following are equivalent: (1) T preserves the… (More)

In this paper, a covariance matrix of circulant correlation, R, is studied. A pattern of entries in R−1 independent of the value ρ of the correlation coefficient is proved based on a recursive… (More)