Matrix Analysis And Applied Linear Algebra

This book avoids the traditional definition-theorem-proof format; instead a fresh approach introduces a variety of problems and examples all in a clear and informal style. The in-depth focus on applications separates this book from others, and helps students to see how linear algebra can be applied to real-life situations. Some of the more contemporary topics of applied linear algebra are included here which are not normally found in undergraduate textbooks. Theoretical developments are always accompanied with detailed examples, and each section ends with a number of exercises from which students can gain further insight. Moreover, the inclusion of historical information provides personal insights into the mathematicians who developed this subject. The textbook contains numerous examples and exercises, historical notes, and comments on numerical performance and the possible pitfalls of algorithms. Solutions to all of the exercises are provided, as well as a CD-ROM containing a searchable copy of the textbook.

Matrix Analysis and Applied Linear Algebra is an honest math text that circumvents the traditional definition-theorem-proof format that has bored students in the past. Meyer uses a fresh approach to introduce a variety of problems and examples ranging from the elementary to the challenging and from simple applications to discovery problems. The focus on applications is a big difference between this book and others. Meyer's book is more rigorous and goes into more depth than some. He includes some of the more contemporary topics of applied linear algebra which are not normally found in undergraduate textbooks. Modern concepts and notation are used to introduce the various aspects of linear equations, leading readers easily to numerical computations and applications. The theoretical developments are always accompanied with examples, which are worked out in detail. Each section ends with a large number of carefully chosen exercises from which the students can gain further insight.

This new book offers a fresh approach to matrix and linear algebra by providing a balanced blend of applications, theory, and computation, while highlighting their interdependence. Intended for a one-semester course, Applied Linear Algebra and Matrix Analysis places special emphasis on linear algebra as an experimental science, with numerous examples, computer exercises, and projects. While the flavor is heavily computational and experimental, the text is independent of specific hardware or software platforms. Throughout the book, significant motivating examples are woven into the text, and each section ends with a set of exercises.

This second edition has been almost completely rewritten to create a textbook designed so instructors can determine the degree of rigor and flexible enough for a one- or two-semester course. The author achieves this by increasing the level of sophistication as the text proceeds from traditional first principles in the early chapters to theory and applications in the later ones, and by ensuring that material at any point is not dependent on subsequent developments. While theorems and proofs are highlighted, the emphasis is on applications. The author provides carefully constructed exercises ranging from easy to moderately challenging to difficult, many of which condition students for topics that follow. An accompanying book, Matrix Analysis and Applied Linear Algebra, Second Edition, Study and Solutions Guide, contains complete solutions and discussions of each exercise; and historical remarks that focus on the personalities of the individuals who created and contributed to the subject's development. This book is designed for use in either a one- or two-term linear algebra course. It can also serve as a reference to anyone who needs to use or apply linear algebra.

This second edition has been almost completely rewritten to create a textbook designed to provide flexibility for nearly any desired degree of rigor and depth of coverage. This is achieved with a linear development ensuring that material at any point is not dependent on subsequent developments and by means of graduated levels of sophistication. The text moves from traditional first principles in early chapters to deeper topics involving both theory and applications in later chapters. This allows for a traditional single-term course based on roughly half of the text without having to refer to more advanced topics while the later portion of the book facilitates a seamless two-term course covering the range of theory and applications generally reserved for discussions beyond fundamentals. Rigor is present throughout, but the level is adaptable because all major theorems have ample accompanying discussions and illustrative examples designed to convince readers and students of the validity of a result without a deep dive into the proof. Moreover, there is an expanded emphasis on both the depth and breadth of applications that are designed to illuminate the utility of the subject across broad areas of science and engineering. At major junctures there are photos and historical remarks concerning the personalities who created and contributed to the subject’s development. Throughout there are carefully constructed exercises ranging from easy to moderately challenging to difficult, many of which condition students for topics that follow.

Advanced undergraduate and first-year graduate students have long regarded this text as one of the best available works on matrix theory in the context of modern algebra. Teachers and students will find it particularly suited to bridging the gap between ordinary undergraduate mathematics and completely abstract mathematics. The first five chapters treat topics important to economics, psychology, statistics, physics, and mathematics. Subjects include equivalence relations for matrixes, postulational approaches to determinants, and bilinear, quadratic, and Hermitian forms in their natural settings. The final chapters apply chiefly to students of engineering, physics, and advanced mathematics. They explore groups and rings, canonical forms for matrixes with respect to similarity via representations of linear transformations, and unitary and Euclidean vector spaces. Numerous examples appear throughout the text.

A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.