{"product_id":"a-combinatorial-approach-to-matrix-theory-and-its-applications-9781420082234","title":"A Combinatorial Approach to Matrix Theory and Its Applications","description":"\u003cp\u003e • Author(s): Richard A. Brualdi | Dragos Cvetkovic\u003cbr\u003e • Publisher: CRC Press\u003cbr\u003e • Publisher Imprint: Chapman and Hall\/CRC\u003cbr\u003e • BISAC: Combinatorics\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eUnlike most elementary books on matrices, \u003cb\u003eA Combinatorial Approach to Matrix Theory and Its Applications\u003c\/b\u003e employs combinatorial and graph-theoretical tools to develop basic theorems of matrix theory, shedding new light on the subject by exploring the connections of these tools to matrices.\u003c\/p\u003e\u003cp\u003eAfter reviewing the basics of graph theory, elementary counting formulas, fields, and vector spaces, the book explains the algebra of matrices and uses the K�nig digraph to carry out simple matrix operations. It then discusses matrix powers, provides a graph-theoretical definition of the determinant using the Coates digraph of a matrix, and presents a graph-theoretical interpretation of matrix inverses. The authors develop the elementary theory of solutions of systems of linear equations and show how to use the Coates digraph to solve a linear system. They also explore the eigenvalues, eigenvectors, and characteristic polynomial of a matrix; examine the important properties of nonnegative matrices that are part of the Perron-Frobenius theory; and study eigenvalue inclusion regions and sign-nonsingular matrices. The final chapter presents applications to electrical engineering, physics, and chemistry. \u003c\/p\u003e\u003cp\u003eUsing combinatorial and graph-theoretical tools, this book enables a solid understanding of the fundamentals of matrix theory and its application to scientific areas.\u003c\/p\u003e","brand":"CRC Press","offers":[{"title":"Hardcover","offer_id":46931693994135,"sku":"9781420082234","price":11654.0,"currency_code":"INR","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9781420082234.webp?v=1771615470","url":"https:\/\/atlanticbooks.com\/products\/a-combinatorial-approach-to-matrix-theory-and-its-applications-9781420082234","provider":"Atlantic Books","version":"1.0","type":"link"}