We study the problem of permuting each column of a given matrix to achieve minimum maximal row sum or maximum minimal row sum, a problem of interest in probability theory and quantitative finance where quantiles of a random variable expressed as the sum of several random variables with unknown dependence structure are estimated. If the minimum maximal row sum is equal to the maximum minimal row...

Abstract The eccentricity matrix ? ( G ) of a graph is obtained from the distance by retaining largest distances in each row and column, leaving zeros remaining ones. energy sum absolute values eigenvalues ). Although matrices graphs are closely related to graphs, number properties substantially different those matrices. change due an edge deletion one such property. In this article, we give ex...

The Line Sum Scaling problem for a nonnegative matrix A is to find positive definite diagonal matrices Y , Z which result in prescribed row and column sums of the scaled matrix Y AZ. The Matrix Balancing problem for a nonnegative square matrix A is to find a positive definite diagonal matrix X such that the row sums in the scaled matrix XAX are equal to the corresponding column sums. We demonst...

An alternating sign matrix is a square matrix such that (i) all entries are 1,-1, or 0, (ii) every row and column has sum 1, and (iii) in every row and column the nonzero entries alternate in sign. Striking numerical evidence of a connection between these matrices and the descending plane partitions introduced by Andrews (Invent. Math. 53 (1979), 193-225) have been discovered, but attempts to p...

We define a higher spin alternating sign matrix to be an integer-entry square matrix in which, for a nonnegative integer r, all complete row and column sums are r, and all partial row and column sums extending from each end of the row or column are nonnegative. Such matrices correspond to configurations of spin r/2 statistical mechanical vertex models with domain-wall boundary conditions. The c...

In this paper, the eigenvalues of row-inverted 2 × 2 Sylvester Hadamard matrices are derived. Especially when the sign of a single row or two rows of a 2×2 Sylvester Hadamard matrix are inverted, its eigenvalues are completely evaluated. As an example, we completely list all the eigenvalues of 256 different row-inverted Sylvester Hadamard matrices of size 8. Mathematics Subject Classification (...

In this paper, based on the numerical relationship between row and column sums, an equivalent representation for double α1-matrices is given by partition of the row and column index sets. As its application, we obtain a subclass of H-matrices and the corresponding (Cassini-type) spectral distribution theorem. And then, we provide a numerical example to illustrates the effectiveness of the new r...

Abstract The group $G = \textrm{GL}_r(k) \times (k^\times )^n$ acts on $\textbf{A}^{r n}$, the space of $r$-by-$n$ matrices: $\textrm{GL}_r(k)$ by row operations and $(k^\times scales columns. A matrix orbit closure is Zariski a point for this action. We prove that class such an in $G$-equivariant $K$-theory n}$ determined matroid generic point. present two formulas class. key to proof show clo...

Abstract We derive a novel stochastic representation of exchangeable Marshall–Olkin distributions based on their death-counting processes. show that these processes are Markov. Furthermore, we provide numerically stable approximation infinitesimal generator matrices in the extendible case. This approach uses integral representations Bernstein functions to calculate generator’s first row, and th...

In this paper, we study the stochastic root matrices of stochastic matrices. All stochastic roots of 2¥2 stochastic matrices are found explicitly. A method based on characteristic polynomial of matrix is developed to find all real root matrices that are functions of the original 3¥3 matrix, including all possible (function) stochastic root matrices. In addition, we comment on some numerical met...