This unique book presents a particularly beautiful way of looking at special relativity. The author encourages students to see beyond the formulas to the deeper structure.The unification of space and time introduced by Einstein’s special theory of relativity is one of the cornerstones of the modern scientific description of the universe. Yet the unification is counterintuitive because we perceive time very differently from space. Even in relativity, time is not just another dimensi...

There are precisely two further generalizations of the real and complex numbers, namely, the quaternions and the octonions. The quaternions naturally describe rotations in three dimensions. In fact, all (continuous) symmetry groups are based on one of these four number systems. This book provides an elementary introduction to the properties of the octonions, with emphasis on their geometric structure. Elementary applications covered include the rotation groups and their spacetime generaliz...

Requiring little more than calculus and some linear algebra, this book provides readers with a coherent path to understanding relativity. It helps readers learn just enough differential geometry to grasp the basics of general relativity. The first half of the book describes some of the surprising implications of relativity without introducing more formalism than necessary. The second half takes a more detailed look at the mathematics of differential forms, showing how they are used to desc...

Boost Your grades with this illustrated Study Guide. You will use it from college all the way to graduate school and beyond.FEATURES:- Clear and concise explanations - Difficult concepts are explained in simple terms - Illustrated with graphs and diagrams TABLE OF CONTENTS:I. Linear equations System of linear equations Determinant Minor Cauchy-Binet formula Cramer's rule Gaussian elimination Gauss-Jordan elimination Strassen algorithm II. Matrices Matrix addition Matrix multiplication Basi...

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 s...

Linear Algebra is intended for a one-term course at the junior or senior level. It begins with an exposition of the basic theory of vector spaces and proceeds to explain the fundamental structure theorems for linear maps, including eigenvectors and eigenvalues, quadric and hermitian forms, diagonalization of symmetric, hermitian, and unitary linear maps and matrices, triangulation, and Jordan canonical form. The book also includes a useful chapter on convex sets and the finite-dimensional ...

Providing a succinct yet comprehensive treatment of the essentials of modern differential geometry and topology, this book's clear prose and informal style make it accessible to advanced undergraduate and graduate students in mathematics and the physical sciences. The text covers the basics of multilinear algebra, differentiation and integration on manifolds, Lie groups and Lie algebras, homotopy and de Rham cohomology, homology, vector bundles, Riemannian and pseudo-Riemannian geometry, a...

A complete introduction to partial differential equations, this textbook provides a rigorous yet accessible guide to students in mathematics, physics and engineering. The presentation is lively and up to date, paying particular emphasis to developing an appreciation of underlying mathematical theory. Beginning with basic definitions, properties and derivations of some basic equations of mathematical physics from basic principles, the book studies first order equations, classification of se...

Matrix Algebra is the first volume of the Econometric Exercises Series. It contains exercises relating to course material in matrix algebra that students are expected to know while enrolled in an (advanced) undergraduate or a postgraduate course in econometrics or statistics. The book contains a comprehensive collection of exercises, all with full answers. But the book is not just a collection of exercises; in fact, it is a textbook, though one that is organized in a completely different m...

At first sight, finitely generated abelian groups and canonical forms of matrices appear to have little in common. However, reduction to Smith normal form, named after its originator H.J.S.Smith in 1861, is a matrix version of the Euclidean algorithm and is exactly what the theory requires in both cases. Starting with matrices over the integers, Part 1 of this book provides a measured introduction to such groups: two finitely generated abelian groups are isomorphic if and only if their inv...

Any student of linear algebra will welcome this textbook, which provides a thorough treatment of this key topic. Blending practice and theory, the book enables the reader to learn and comprehend the standard methods, with an emphasis on understanding how they actually work. At every stage, the authors are careful to ensure that the discussion is no more complicated or abstract than it needs to be, and focuses on the fundamental topics. The book is ideal as a course text or for self-study. ...

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 their properties a simple matter, and in practical applications such software is often essential. However, using this tool when learning about matrices, without first gaining a proper understanding of the underlying theory, limits the ability to use matrices and to apply them to new problems. ...