This book focuses the solutions of linear algebra and matrix analysis problems, with the exclusive use of MATLAB. The topics include representations, fundamental analysis, transformations of ...matrices, matrix equation solutions as well as matrix functions. Attempts on matrix and linear algebra applications are also explored.
Linear Algebra Shen, Li-Yong; Wang, Haohao; Wojdylo, Jerzy
2019.
eBook
The aim of this book is two-fold: to introduce the fundamental concepts of linear algebra and to apply the theorems in computation-oriented applications. --
This is one book that can genuinely be said to be straight from the horse's mouth. Written by the originator of the technique, it examines parallel coordinates as the leading methodology for ...multidimensional visualization. Starting from geometric foundations, this is the first systematic and rigorous exposition of the methodology's mathematical and algorithmic components. It covers, among many others, the visualization of multidimensional lines, minimum distances, planes, hyperplanes, and clusters of "near" planes. The last chapter explains in a non-technical way the methodology's application to visual and automatic data mining. The principles of the latter, along with guidelines, strategies and algorithms are illustrated in detail on real high-dimensional datasets.
In this article, the Gershgorin disk theorem in complex interval matrices is proposed for enclosing interval eigenvalues. This is a non-iterative method for finding eigenvalue bounds for both real ...and imaginary parts. Moreover, we are able to find gaps between the clusters of interval eigenvalues and have compared the results with the previous theorems for interval eigenvalue bounds for complex interval matrices. These results can be decisive for checking Hurwitz and Schur stability of complex interval matrices that appear in uncertain dynamical systems. Further bounds obtained from the present formulae can be considered as the initial bounds for iterative methods. Key words: complex interval matrices, Gershgorin disk theorem, interval eigenvalues, eigenvalue bounds.
The goal of this book is three-fold: it describes the basics of model order reduction and related aspects. In numerical linear algebra, it covers both general and more specialized model order ...reduction techniques for linear and nonlinear systems, and it discusses the use of model order reduction techniques in a variety of practical applications. The book contains many recent advances in model order reduction, and presents several open problems for which techniques are still in development. It will serve as a source of inspiration for its readers, who will discover that model order reduction is a very exciting and lively field.
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