Cadastral space may be the object of legal, geometric and topological analyses. Topological aspects, which are least recognized by the users, are deployed by IT specialists in the process of developing analytical applications. This study attempts to analyze the theoretical aspects of cadastral-topological space. Algebraic topology delivers a new approach by using a single mathematical formula t...

In this paper, the shape decomposition problem is addressed as a solution of an appropriately constrained Nonnegative Matrix Factorization Problem (NMF). Inspired from an idealization of the visibility matrix having a block diagonal form, special requirements while formulating the NMF problem are taken into account. Starting from a contaminated observation matrix, the objective is to reveal its...

For a Hermitian matrix with its main block diagonal given, this paper shows how to choose the off-diagonal blocks such that the resulting matrix has the maximal and minimal possible ranks and inertias, respectively. Some direct consequences and applications are also given.

The multigrid method is used for coupled fluid-solid scattering discretized by linear finite elements. Numerical results show that using Krylov methods as smoothers allows coarser spaces than with standard smoothers, such as Jacobi and GaussSeidel. Block diagonal preconditioning for the 2 × 2 block diagonal matrix of the coupled system is also considered. Both multigrid and block diagonal preco...

A special structure of a kind of matrices, r−block monomial and r−block diagonal matrices, is introduced. Theirs nonnegative Drazin inverses have been studied. The influence of these matrices on the positiveness of the trajectory of a descriptor system has been analyzed. Key–Words:Drazin inverse, nonnegative matrix, block monomial matrix, descriptor system.

For a Hermitian matrix with its main block diagonal given, this paper shows how to choose the off-diagonal blocks such that the resulting matrix has the maximal and minimal possible ranks and inertias, respectively. Some direct consequences and applications are also given.

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 .

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 .

The paper proposes an algorithm which computes a (2 × 2) block partition of an irreducible, sparse matrix with a zero-free diagonal so that one of the diagonal blocks is triangular. The algorithm works by computing a cutset of the directed graph associated with the off-diagonal part of the matrix and is linear in the number of nonzeros therein. The proposed algorithm is then extended to reducib...

We provide a proof that entanglement of any density matrix which is block diagonal in subspaces are disjoint terms the Hilbert space one two potentially entangled subsystems can simply be calculated as weighted average present within each block. This especially useful for thermal-equilibrium states always inherit symmetries Hamiltonian, since block-diagonal Hamiltonians common, interactions inv...