A Combinatorial Approach to Matrix Theory and Its Applications

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Through combinatorial and graph theoretic tools, this self-contained reference helps readers understand the fundamentals of matrix theory and its applications to science. It develops the theory using graphs to explain the basic matrix construction, formulas, computations, ideas, and results. The authors stress the combinatorial aspects of the topics with other aspects of the theory. Containing material rarely found at this level, the book covers Gersgorin's theorem and extensions, Kronecker product of matrices, sign nonsingular matrices, and evaluation of the permanent. It also includes various exercises.