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On the generalized Riccati matrix differential equation. Exact, approximate solutions and error estimate

Lucas Jódar, Enrique A. Navarro (1989)

Aplikace matematiky

In this paper explicit expressions for solutions of Cauchy problems and two-point boundary value problems concerned with the generalized Riccati matrix differential equation are given. These explicit expressions are computable in terms of the data and solutions of certain algebraic Riccati equations related to the problem. The interplay between the algebraic and the differential problems is used in order to obtain approximate solutions of the differential problem in terms of those of the algebraic...

On the inertia sets of some symmetric sign patterns

C. M. da Fonseca (2006)

Czechoslovak Mathematical Journal

A matrix whose entries consist of elements from the set { + , - , 0 } is a sign pattern matrix. Using a linear algebra theoretical approach we generalize of some recent results due to Hall, Li and others involving the inertia of symmetric tridiagonal sign matrices.

On the inverse of the adjacency matrix of a graph

Alexander Farrugia, John Baptist Gauci, Irene Sciriha (2013)

Special Matrices

A real symmetric matrix G with zero diagonal encodes the adjacencies of the vertices of a graph G with weighted edges and no loops. A graph associated with a n × n non–singular matrix with zero entries on the diagonal such that all its (n − 1) × (n − 1) principal submatrices are singular is said to be a NSSD. We show that the class of NSSDs is closed under taking the inverse of G. We present results on the nullities of one– and two–vertex deleted subgraphs of a NSSD. It is shown that a necessary...

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