Matrices and Matroids for Systems Analysis - Murota, Kazuo; SpringerLink (Online service) (Berlin, Heidelberg : Springer Berlin Heidelberg, 2010)
A matroid is an abstract mathematical structure that captures combinatorial properties of matrices. This book offers a unique introduction to matroid theory, emphasizing motivations from matrix theory and applications to systems analysis. This book serves also as a comprehensive presentation of the theory and application of mixed matrices, developed primarily by the present author in the 1990's. A mixed matrix is a convenient mathematical tool for systems analysis, compatible with the physical observation that "fixed constants" and "system parameters" are to be distinguished in the description of engineering systems. This book will be extremely useful to graduate students and researchers in engineering, mathematics and computer science. From the reviews: " The book has been prepared very carefully, contains a lot of interesting results and is highly recommended for graduate and postgraduate students." András Recski, Mathematical Reviews Clippings 2000m:93006
to Structural Approach Overview of the Book -- Matrix, Graph, and Matroid -- Physical Observations for Mixed Matrix Formulation -- Theory and Application of Mixed Matrices -- Polynomial Matrix and Valuated Matroid -- Theory and Application of Mixed Polynomial Matrices -- Further Topics.
Keywords: Mathematics; Chemical engineering; Computer software; Matrix theory; Combinatorics; Engineering mathematics; Mathematics; Combinatorics; Linear and Multilinear Algebras, Matrix Theory; Appl.Mathematics/Computational Methods of Engineering; Industrial Chemistry/Chemical Engineering; Algorithm Analysis and Problem Complexity