Showing papers by "Richard A. Brualdi published in 2008"
Book•
06 Aug 2008TL;DR: In this paper, the Konig Digraph of a Matrix Partitioned Matrices Powers of Matrices Matrix Powers and Digraphs Circulant Matrices Permutations with Restrictions Determinants Definition of the Determinant properties of determinants A Special Determinante Formula Classical Definition of DeterminANT Laplace Development of the determinant Matrix Inverses Adjoint and Its Determinent Inverse of a Square Matrix Graph-Theoretic Interpretation Systems of Linear Equations Solutions of Linear Systems Cramer's Formula Solving Linear Systems by Digraph
Abstract: Introduction Graphs Digraphs Some Classical Combinatorics Fields Vector Spaces Basic Matrix Operations Basic Concepts The Konig Digraph of a Matrix Partitioned Matrices Powers of Matrices Matrix Powers and Digraphs Circulant Matrices Permutations with Restrictions Determinants Definition of the Determinant Properties of Determinants A Special Determinant Formula Classical Definition of the Determinant Laplace Development of the Determinant Matrix Inverses Adjoint and Its Determinant Inverse of a Square Matrix Graph-Theoretic Interpretation Systems of Linear Equations Solutions of Linear Systems Cramer's Formula Solving Linear Systems by Digraphs Signal Flow Digraphs of Linear Systems Sparse Matrices Spectrum of a Matrix Eigenvectors and Eigenvalues The Cayley-Hamilton Theorem Similar Matrices and the JCF Spectrum of Circulants Nonnegative Matrices Irreducible and Reducible Matrices Primitive and Imprimitive Matrices The Perron-Frobenius Theorem Graph Spectra Additional Topics Tensor and Hadamard Product Eigenvalue Inclusion Regions Permanent and Sign-Nonsingular Matrices Applications Electrical Engineering: Flow Graphs Physics: Vibration of a Membrane Chemistry: Unsaturated Hydrocarbons Exercises appear at the end of each chapter.
107 citations
TL;DR: In this paper, it was shown that the Brualdi condition can be tested and, in polynomial time, a diagonal matrix D, with positive diagonal entries, such that AD (where A is any nonnnegative matrix satisfying the conditions) is strictly diagonally dominant (and so, A is nonsingular).
3 citations
TL;DR: In this paper, the Jordan canonical form has the largest number of off-diagonal zero entries among all the matrices that are similar to a given square complex matrix, and it is shown that such matrices can be characterized.
3 citations
TL;DR: In this paper, the authors investigated the connection between isolated sets of diagonals of a matrix and simplicial faces of the polytope Ω n of doubly stochastic matrices.
Abstract: We investigate a connection between isolated sets of diagonals of a matrix and simplicial faces of the polytope Ω n of doubly stochastic matrices. We also consider the minimum permanent on simplicial faces of Ω n .
1 citations
TL;DR: In this paper, it was shown that trees and bipartite graphs with a vertex of degree 1 or of diameter at least 9 have a symmetric (0, 1)-approximation.
1 citations