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This is the first book on analytic hyperbolic geometry, fully analogous to analytic Euclidean geometry. Analytic hyperbolic geometry regulates relativistic mechanics just as analytic Euclidean geometry regulates classical mechanics. The book presents a novel gyrovector space approach to analytic hyperbolic geometry, fully analogous to the well-known vector space approach to Euclidean geometry. A gyrovector is a hyperbolic vector. Gyrovectors are equivalence classes of directed gyrosegments that add according to the gyroparallelogram law just as vectors are equivalence classes of directed segme

Geometry, Hyperbolic --- Vector algebra --- Algebra, Vector --- Algebras, Linear --- Vector analysis --- Hyperbolic geometry --- Lobachevski geometry --- Lobatschevski geometry --- Geometry, Non-Euclidean

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"Many books in linear algebra focus purely on getting students through exams, but this text explains both the how and the why of linear algebra and enables students to begin thinking like mathematicians. The author demonstrates how different topics (geometry, abstract algebra, numerical analysis, physics) make use of vectors in different ways and how these ways are connected, preparing students for further work in these areas. The book is packed with hundreds of exercises ranging from the routine to the challenging. Sketch solutions of the easier exercises are available online"--

Vector algebra. --- Algebras, Linear. --- Linear algebra --- Algebra, Universal --- Generalized spaces --- Mathematical analysis --- Calculus of operations --- Line geometry --- Topology --- Algebra, Vector --- Algebras, Linear --- Vector analysis

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Vector algebra --- Problems, exercises, etc. --- -512.64 --- Algebra, Vector --- Algebras, Linear --- Vector analysis --- Problems, exercises, etc --- Linear and multilinear algebra. Matrix theory --- 512.64 Linear and multilinear algebra. Matrix theory --- 512.64 --- Vector algebra - Problems, exercises, etc.

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Algebra --- Vector algebra --- Vector analysis --- 514.7 --- Algebra, Universal --- Mathematics --- Numbers, Complex --- Quaternions --- Spinor analysis --- Algebra, Vector --- Algebras, Linear --- Differential geometry. Algebraic and analytic methods in geometry --- Vector algebra. --- Vector analysis. --- 514.7 Differential geometry. Algebraic and analytic methods in geometry

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It is true that there exist many books dedicated to linear algebra and some­ what fewer to multilinear algebra, written in several languages, and perhaps one can think that no more books are needed. However, it is also true that in algebra many new results are continuously appearing, different points of view can be used to see the mathematical objects and their associated structures, and different orientations can be selected to present the material, and all of them deserve publication. Under the leadership of Juan Ramon Ruiz-Tolosa, Professor of multilin­ ear algebra, and the collaboration of Enrique Castillo, Professor of applied mathematics, both teaching at an engineering school in Santander, a tensor textbook has been born, written from a practical point of view and free from the esoteric language typical of treatises written by algebraists, who are not interested in descending to numerical details. The balance between follow­ ing this line and keeping the rigor of classical theoretical treatises has been maintained throughout this book. The book assumes a certain knowledge of linear algebra, and is intended as a textbook for graduate and postgraduate students and also as a consultation book. It is addressed to mathematicians, physicists, engineers, and applied scientists with a practical orientation who are looking for powerful tensor tools to solve their problems.

Calculus of tensors --- Tensor algebra --- Vector algebra --- Algebra, Vector --- Algebras, Linear --- Vector analysis --- Algebra, Tensor --- Tensor products --- Absolute differential calculus --- Analysis, Tensor --- Calculus, Absolute differential --- Calculus, Tensor --- Tensor analysis --- Tensor calculus --- Geometry, Differential --- Geometry, Infinitesimal --- Spinor analysis --- Information theory. --- Algebra. --- Physics. --- Matrix theory. --- Engineering mathematics. --- Theory of Computation. --- Physics, general. --- Linear and Multilinear Algebras, Matrix Theory. --- Theoretical, Mathematical and Computational Physics. --- Mathematical and Computational Engineering. --- Engineering --- Engineering analysis --- Mathematical analysis --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Mathematics --- Communication theory --- Communication --- Cybernetics --- Computers. --- Mathematical physics. --- Applied mathematics. --- Physical mathematics --- Physics --- Automatic computers --- Automatic data processors --- Computer hardware --- Computing machines (Computers) --- Electronic brains --- Electronic calculating-machines --- Electronic computers --- Hardware, Computer --- Computer systems --- Machine theory --- Calculators --- Cyberspace