Matrix Algebra

This unique text provides students with a basic course in both calculus and analytic geometry. It promotes an intuitive approach to calculus and emphasizes algebraic concepts. Minimal prerequisites. N

This revision of a well-known text includes more sophisticated mathematical material. A new section on applications provides an introduction to the modern treatment of calculus of several variables, a

Linear algebra and the study of matrix algorithms have become fundamental to the development of statistical models. Using a vector-space approach, this book provides an understanding of the major conc

The Weyr matrix canonical form is a largely unknown cousin of the Jordan canonical form. Discovered by Eduard Weyr in 1885, the Weyr form outperforms the Jordan form in a number of mathematical situat

Engineers and scientists need to have an introduction to the basics of linear algebra in a context they understand. Computer algebra systems make the manipulation of matrices and the determination of

Linear algebra and matrix theory are fundamental tools in mathematical and physical science, as well as fertile fields for research. This second edition of this acclaimed text presents results of both classic and recent matrix analysis using canonical forms as a unifying theme and demonstrates their importance in a variety of applications. This thoroughly revised and updated second edition is a text for a second course on linear algebra and has more than 1,100 problems and exercises, new sections on the singular value and CS decompositions and the Weyr canonical form, expanded treatments of inverse problems and of block matrices, and much more.

Linear algebra and matrix theory are fundamental tools in mathematical and physical science, as well as fertile fields for research. This second edition of this acclaimed text presents results of both classic and recent matrix analysis using canonical forms as a unifying theme and demonstrates their importance in a variety of applications. This thoroughly revised and updated second edition is a text for a second course on linear algebra and has more than 1,100 problems and exercises, new sections on the singular value and CS decompositions and the Weyr canonical form, expanded treatments of inverse problems and of block matrices, and much more.

This is the second volume in a projected five-volume survey of numerical linear algebra and matrix algorithms. Stressing depth over breadth, Professor Stewart treats the derivation and implementation

The aim of this book is to concisely present fundamental ideas, results, and techniques in linear algebra and mainly matrix theory. The book contains ten chapters covering various topics ranging from

The fourth edition of Gene H. Golub and Charles F. Van Loan's classic is an essential reference for computational scientists and engineers in addition to researchers in the numerical linear algebra co

This edited volume highlights the scientific contributions of Volker Mehrmann, a leading expert in the area of numerical (linear) algebra, matrix theory, differential-algebraic equations and control t

This text provides an introduction to numerical linear algebra together with its application to solving certain problems arising in state-space control and systems theory, including statistical condit

This book, first published in 1991, is devoted to the exposition of combinatorial matrix theory. This subject concerns itself with the use of matrix theory and linear algebra in proving results in combinatorics (and vice versa), and with the intrinsic properties of matrices viewed as arrays of numbers rather than algebraic objects in themselves. There are chapters dealing with the many connections between matrices, graphs, digraphs and bipartite graphs. The basic theory of network flows is developed in order to obtain existence theorems for matrices with prescribed combinatorial properties and to obtain various matrix decomposition theorems. Other chapters cover the permanent of a matrix, and Latin squares. The final chapter deals with algebraic characterizations of combinatorial properties and the use of combinatorial arguments in proving classical algebraic theorems, including the Cayley-Hamilton Theorem and the Jordan Canonical Form. The book is sufficiently self-contained for use

This book, first published in 1991, is devoted to the exposition of combinatorial matrix theory. This subject concerns itself with the use of matrix theory and linear algebra in proving results in combinatorics (and vice versa), and with the intrinsic properties of matrices viewed as arrays of numbers rather than algebraic objects in themselves. There are chapters dealing with the many connections between matrices, graphs, digraphs and bipartite graphs. The basic theory of network flows is developed in order to obtain existence theorems for matrices with prescribed combinatorial properties and to obtain various matrix decomposition theorems. Other chapters cover the permanent of a matrix, and Latin squares. The final chapter deals with algebraic characterizations of combinatorial properties and the use of combinatorial arguments in proving classical algebraic theorems, including the Cayley-Hamilton Theorem and the Jordan Canonical Form. The book is sufficiently self-contained for use

A unique, applied approach to problem solving in linear algebraDeparting from the standard methods of analysis, this unique book presents methodologies and algorithms based on the concept of orthogona

Covers determinants, linear spaces, systems of linear equations, linear functions of a vector argument, coordinate transformations, the canonical form of the matrix of a linear operator, bilinear and

This self-contained textbook takes a matrix-oriented approach to linear algebra and presents a complete theory, including all details and proofs, culminating in the Jordan canonical form and its proof

Building on the foundations of its predecessor volume, Matrix Analysis, this book treats in detail several topics in matrix theory not included in the previous volume, but with important applications and of special mathematical interest. As with the previous volume, the authors assume a background knowledge of elementary linear algebra and rudimentary analytical concepts. Many examples and exercises of varying difficulty are included.

This book provides a self-contained and accessible introduction to linear and multilinear algebra. Besides the standard techniques for linear and multilinear algebra many advanced topics are included.

As discrete models and computing have become more common, there is a need to study matrix computation and numerical linear algebra. Encompassing a diverse mathematical core, Elements of Matrix Modelin

Linear algebra and matrix theory are essentially synonymous terms for an area of mathematics that has become one of the most useful and pervasive tools in a wide range of disciplines. It is also a sub

This book encourages readers to develop an intuitive understanding of the foundations of Linear Algebra. An emphasis on the concepts of Linear Algebra and Matrix Theory conveys the structure and natur

Designed for use in a second course on linear algebra, Matrix Theory and Applications with MATLAB covers the basics of the subject-from a review of matrix algebra through vector spaces to matrix calcu

With this text, basic quantum mechanics becomes accessible to undergraduates with no background in mathematics beyond algebra. Containing more than 100 problems, it provides an easy way to learn part

This book provides a blend of undergraduate- and graduate-level topics in matrix theory and linear algebra and provides an often-needed bridge between undergraduate-level courses and the level of matr

Based on the recommendations of the Linear Algebra Curriculum Study Group, this introduction to linear algebra offers a matrix-oriented approach with more emphasis on problem solving and applications.

This is a matrix-oriented approach to linear algebra that covers the traditional material of the courses generally known as “Linear Algebra I” and “Linear Algebra II” throughout North America, but it

This is a matrix-oriented approach to linear algebra that covers the traditional material of the courses generally known as “Linear Algebra I” and “Linear Algebra II” throughout North America, but it

Linear algebra is something all mathematics undergraduates and many other students, in subjects ranging from engineering to economics, have to learn. The fifth edition of this hugely successful textbook retains the quality of earlier editions while at the same time seeing numerous minor improvements and major additions. The latter include: a new chapter on singular values and singular vectors, including ways to analyze a matrix of data; a revised chapter on computing in linear algebra, with professional-level algorithms and code that can be downloaded for a variety of languages; a new section on linear algebra and cryptography; and a new chapter on linear algebra in probability and statistics. A dedicated and active website also offers solutions to exercises as well as new exercises from many different sources (e.g. practice problems, exams, development of textbook examples), plus codes in MATLAB, Julia, and Python.

The renowned mathematician and educator Gilbert Strang presents a collection of expository papers on the theory and applications of linear algebra, accompanied by video lectures on http://ocw.mit.edu. The essays are diverse in scope and range from purely theoretical studies on deep fundamental principles of matrix algebra to discussions on the teaching of calculus and an examination of the mathematical foundations of aspects of computational engineering. One thing these essays have in common is the way that they express both the importance and the beauty of the subject, as well as the author's passion for mathematics. This text will be of practical use to students and researchers across a whole spectrum of numerate disciplines. Furthermore, this collection provides a unique perspective on mathematics and the communication thereof as a human endeavour, complemented as these essays are by commentary from the author regarding their provenance and the reaction to them.

This book provides an overview of the mathematical foundations of polarimetry, covering relevant areas of polarization algebra as well as the mathematical methods for exploiting polarimetric measureme

Computation of General Matrix Inverses and Applications offers a gradual exposition to matrix theory as a subject of linear algebra. It presents both the theoretical results in generalized matrix inve

This volume deals with advanced topics in matrix theory using the notions and tools from algebra, analysis, geometry, and numerical analysis. It consists of seven chapters that are loosely connected.

This volume deals with advanced topics in matrix theory using the notions and tools from algebra, analysis, geometry, and numerical analysis. It consists of seven chapters that are loosely connected.

This monograph arose from lectures at the University of Oklahoma on topics related to linear algebra over commutative rings. It provides an introduction of matrix theory over commutative rings. The mo

For introductory sophomore-level courses in Linear Algebra or Matrix Theory. This title is part of the Pearson Modern Classics series. Pearson Modern Classics are acclaimed titles at a value pr

This textbook provides an introduction to abstract algebra for advanced undergraduate students. Based on the authors' notes at the Department of Mathematics, National Chung Cheng University, it contains material sufficient for three semesters of study. It begins with a description of the algebraic structures of the ring of integers and the field of rational numbers. Abstract groups are then introduced. Technical results such as Lagrange's theorem and Sylow's theorems follow as applications of group theory. The theory of rings and ideals forms the second part of this textbook, with the ring of integers, the polynomial rings and matrix rings as basic examples. Emphasis will be on factorization in a factorial domain. The final part of the book focuses on field extensions and Galois theory to illustrate the correspondence between Galois groups and splitting fields of separable polynomials.Three whole new chapters are added to this second edition. Group action is introduced to give a more i

Covers vectors, matrix algebra, linear-algebra, linear-equations, determinants, mappings, canonical forms, linear functions, and quadratic forms