To analyze the limiting spectral distribution of some random blockmatrices, Girko [7] uses a system of canonical equations from [6]. In this paper, we use the method of moments to give an integral form for the almost sure limiting spectral distribution of such matrices.

We characterize the pseudo-equivalence of a block lower triangular matrix T = [Tij ] over a regular ring, and its block diagonal matrix D(T ) = [Tii], in terms of suitable Roth consistency conditions. The latter can in turn be expressed in terms of the solvability of certain matrix equations of the form TiiX − Y Tjj = Uij .

We present some observations on the block triangular form (btf) of structurally symmetric, square, sparse matrices. If the matrix is structurally rank deficient, its canonical btf has at least one underdetermined and one overdetermined block. We prove that these blocks are transposes of each other. We further prove that the square block of the canonical btf, if present, has a special fine struc...

the focus of this paper is to consider the compressed sensing problem. it is stated that the compressed sensing theory, under certain conditions, helps relax the nyquist sampling theory and takes smaller samples. one of the important tasks in this theory is to carefully design measurement matrix (sampling operator). most existing methods in the literature attempt to optimize a randomly initiali...

In this paper we consider discrete-time multidimensional Markov chains having a block transition probability matrix which is the sum of a matrix with repeating block rows and a matrix of upper-Hessenberg, quasi-Toeplitz structure. We derive sufficient conditions for the existence of the stationary distribution, and outline two algorithms for calculating the stationary distribution.

We propose a BB identification by simultaneity matrix (BISM) algorithm. The input is a set of -bit solutions denoted by S. The number of solutions is denoted by n = |S|. The output is a partition of bit positions {0, . . . , − 1}. The BISM is composed of Simultaneity-Matrix-Construction and Fine-Valid-Partition algorithms. Algorithm SMC is outlined as follows (aij denotes the matrix element at ...

A general method is presented for establishing universal factorization equalities for 2×2 and 4×4 block matrices. As applications, some universal factorization equalities for matrices over four-dimensional algebras are established, in particular, over the Hamiltonian quaternion algebra.

  We consider the two well knownminimax and minisum single facility location problems in the plane which has been divided into two regions, and by a straight line. The two regions are measured by various norms . We focus on three special cases in which the regions and are measured by and norms, and block norms, two distinct block norms. Based on the properties of block norms then we use linear ...

The pseudo-equivalence of a block lower triangular matrix T = [Tij ] over a regular ring and its block diagonal matrix D(T ) = [Tii] is characterized in terms of suitable Roth consistency conditions. The latter can in turn be expressed in terms of the solvability of certain matrix equations of the form TiiX − Y Tjj = Uij .

Many types of pairwise interaction take the form of a fixed set of nodes with edges that appear and disappear over time. In the case of discrete-time evolution, the resulting evolving network may be represented by a time-ordered sequence of adjacency matrices. We consider here the issue of representing the system as a single, higher dimensional block matrix, built from the individual time-slice...