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...

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...

Heyman gives an interesting factorization of I ? P , where P is the transition probability matrix for an ergodic Markov Chain. We show that this factoriza-tion is valid if and only if the Markov chain is recurrent. Moreover, we provide a decomposition result which includes all ergodic, null recurrent as well as the transient Markov chains as special cases. Such a decomposition has been shown to...

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 Two matrices $$H_1$$ H 1 and $$H_2$$ 2 with entries from a multiplicative group G are said to be monomially equivalent, denoted by $$H_1\cong H_2$$ ≅ , if one of the can obtained other via sequence row co...

We derive expressions for the average distance distributions in several ensembles of regular low-density parity-check codes (LDPC). Among these ensembles are the standard one defined by matrices having given column and row sums, ensembles defined by matrices with given column sums or given row sums, and an ensemble defined by bipartite graphs.

In 1981, G. D. James proved two theorems about the decomposition matrices of Schur algebras involving the removal of the first row or column from a Young diagram. He established corresponding results for the symmetric group using the Schur functor. We apply James’ techniques to prove that row removal induces an injection on the corresponding Ext between simple modules for the Schur algebra. We ...