Provides One Unified Formula That Gives Solutions to Several Types of GSEsGeneralized Sylvester equations (GSEs) are applied in many fields, including applied mathematics, systems and control, and signal processing. Generalized Sylvester Equations: Unified Parametric Solutions presents a unified parametric approach for solving various types of GSEs

Abstract: "In this note we show how to compute the minimum-norm, least squares solution of the generalized Sylvester equation AX+YB=C,"

In 1990, the National Science Foundation recommended that every college mathematics curriculum should include a second course in linear algebra. In answer to this recommendation, Matrix Theory: From Generalized Inverses to Jordan Form provides the material for a second semester of linear algebra that probes introductory linear algebra concepts while also exploring topics not typically covered in a sophomore-level class. Tailoring the material to advanced undergraduate and beginning graduate students, the authors offer instructors flexibility in choosing topics from the book. The text first focuses on the central problem of linear algebra: solving systems of linear equations. It then discusses LU factorization, derives Sylvester's rank formula, introduces full-rank factorization, and describes generalized inverses. After discussions on norms, QR factorization, and orthogonality, the authors prove the important spectral theorem. They also highlight the primary decomposition theorem, Schur's triangularization theorem, singular value decomposition, and the Jordan canonical form theorem. The book concludes with a chapter on multilinear algebra. With this classroom-tested text students can delve into elementary linear algebra ideas at a deeper level and prepare for further study in matrix theory and abstract algebra.

Numerical Methods for Linear Control Systems Design and Analysis is an interdisciplinary textbook aimed at systematic descriptions and implementations of numerically-viable algorithms based on well-established, efficient and stable modern numerical linear techniques for mathematical problems arising in the design and analysis of linear control systems both for the first- and second-order models. - Unique coverage of modern mathematical concepts such as parallel computations, second-order systems, and large-scale solutions - Background material in linear algebra, numerical linear algebra, and control theory included in text - Step-by-step explanations of the algorithms and examples

Matrix Algorithms in MATLAB focuses on the MATLAB code implementations of matrix algorithms. The MATLAB codes presented in the book are tested with thousands of runs of MATLAB randomly generated matrices, and the notation in the book follows the MATLAB style to ensure a smooth transition from formulation to the code, with MATLAB codes discussed in this book kept to within 100 lines for the sake of clarity. The book provides an overview and classification of the interrelations of various algorithms, as well as numerous examples to demonstrate code usage and the properties of the presented algorithms. Despite the wide availability of computer programs for matrix computations, it continues to be an active area of research and development. New applications, new algorithms, and improvements to old algorithms are constantly emerging. - Presents the first book available on matrix algorithms implemented in real computer code - Provides algorithms covered in three parts, the mathematical development of the algorithm using a simple example, the code implementation, and then numerical examples using the code - Allows readers to gain a quick understanding of an algorithm by debugging or reading the source code - Includes downloadable codes on an accompanying companion website, www.matrixalgorithmsinmatlab.com, that can be used in other software development

A thorough and elegant treatment of the theory of matrix functions and numerical methods for computing them, including an overview of applications, new and unpublished research results, and improved algorithms. Key features include a detailed treatment of the matrix sign function and matrix roots; a development of the theory of conditioning and properties of the Fre;chet derivative; Schur decomposition; block Parlett recurrence; a thorough analysis of the accuracy, stability, and computational cost of numerical methods; general results on convergence and stability of matrix iterations; and a chapter devoted to the f(A)b problem. Ideal for advanced courses and for self-study, its broad content, references and appendix also make this book a convenient general reference. Contains an extensive collection of problems with solutions and MATLAB implementations of key algorithms.

Quaternions are a number system that has become increasingly useful for representing the rotations of objects in three-dimensional space and has important applications in theoretical and applied mathematics, physics, computer science, and engineering. This is the first book to provide a systematic, accessible, and self-contained exposition of quaternion linear algebra. It features previously unpublished research results with complete proofs and many open problems at various levels, as well as more than 200 exercises to facilitate use by students and instructors. Applications presented in the book include numerical ranges, invariant semidefinite subspaces, differential equations with symmetries, and matrix equations. Designed for researchers and students across a variety of disciplines, the book can be read by anyone with a background in linear algebra, rudimentary complex analysis, and some multivariable calculus. Instructors will find it useful as a complementary text for undergraduate linear algebra courses or as a basis for a graduate course in linear algebra. The open problems can serve as research projects for undergraduates, topics for graduate students, or problems to be tackled by professional research mathematicians. The book is also an invaluable reference tool for researchers in fields where techniques based on quaternion analysis are used.

This book constitutes the refereed proceedings of the 37th Computer Graphics International Conference, CGI 2020, held in Geneva, Switzerland, in October 2020. The conference was held virtually. The 43 full papers presented together with 3 short papers were carefully reviewed and selected from 189 submissions. The papers address topics such as: virtual reality; rendering and textures; augmented and mixed reality; video processing; image processing; fluid simulation and control; meshes and topology; visual simulation and aesthetics; human computer interaction; computer animation; geometric computing; robotics and vision; scientific visualization; and machine learning for graphics.

Comprehensive account of theory and applications of Gröbner bases, co-edited by the subject's inventor.