The Handbook of Linear Algebra provides comprehensive coverage of linear algebra concepts, applications, and computational software packages in an easy-to-use handbook format. The esteemed international contributors guide you from the very elementary aspects of the subject to the frontiers of current research. The five main parts of the book encompass the fundamentals of linear algebra; combinatorial and numerical linear algebra; applications of linear algebra to various mathematical and nonmathematical disciplines, such as quantum computing, control theory, signal processing, and computational biology; and software packages for linear algebra computations, including MATLAB®, Maple™, and Mathematica®.

A unique treatment of signal processing using a model-based perspective Signal processing is primarily aimed at extracting useful information, while rejecting the extraneous from noisy data. If signal levels are high, then basic techniques can be applied. However, low signal levels require using the underlying physics to correct the problem causing these low levels and extracting the desired information. Model-based signal processing incorporates the physical phenomena, measurements, and noise in the form of mathematical models to solve this problem. Not only does the approach enable signal processors to work directly in terms of the problem's physics, instrumentation, and uncertainties, but it provides far superior performance over the standard techniques. Model-based signal processing is both a modeler's as well as a signal processor's tool.

Have you ever wondered why the language of modern physics centres on geometry? Or how quantum operators and Dirac brackets work? What a convolution really is? What tensors are all about? Or what field theory and lagrangians are, and why gravity is described as curvature?
This book takes you on a tour of the main ideas forming the language of modern mathematical physics. Here you will meet novel approaches to concepts such as determinants and geometry, wave function evolution, statistics, signal processing, and three-dimensional rotations. You'll see how the accelerated frames of special relativity tell us about gravity. On the journey, you'll discover how tensor notation relates to vector calculus, how differential geometry is built on intuitive concepts, and how variational calculus leads to field theory. You will meet quantum measurement theory, along with Green functions and the art of complex integration, and finally general relativity and cosmology.

This book is a thoughtful exposition of the algebra and calculus of differential forms, the Clifford and Spin-Clifford bundles formalisms with emphasis in calculation procedures, and vistas to a formulation of some important concepts of differential geometry necessary for a deep understanding of spacetime physics. The formalism discloses the hidden geometrical nature of spinor fields. Maxwell, Dirac and Einstein fields, which were originally considered objects of a very different mathematical nature, are shown to have representatives as objects of the same mathematical nature, i.e. as sections of an appropriate Clifford bundle. This approach reveals unity in the diversity and also the many faces of the equations satisfied by those fields. Moreover, it suggests relationships which are hidden in the standard formalisms and new paths for research. Some foundational issues of relativistic field theories, in particular the one concerning the conditions for the existence of the conservation laws of energy-momentum and angular momentum in spacetime theories and many misconceptions concerning this issue is analyzed in details.

This is the only book on spectral methods built around MATLAB programs. Along with finite differences and finite elements, spectral methods are one of the three main technologies for solving partial differential equations on computers. Since spectral methods involve significant linear algebra and graphics they are very suitable for the high level programming of MATLAB. This hands-on introduction is built around forty short and powerful MATLAB programs, which the reader can download from the World Wide Web. This book presents the key ideas along with many figures, examples, and short, elegant MATLAB programs for readers to adapt to their own needs. It covers ODE and PDE boundary value problems, eigenvalues and pseudospectra, linear and nonlinear waves, and numerical quadrature.

In image processing, "motions by curvature" provide an efficient way to smooth curves representing the boundaries of objects. In such a motion, each point of the curve moves, at any instant, with a normal velocity equal to a function of the curvature at this point. This book is a rigorous and self-contained exposition of the techniques of "motion by curvature". The approach is axiomatic and formulated in terms of geometric invariance with respect to the position of the observer. This is translated into mathematical terms, and the author develops the approach of Olver, Sapiro and Tannenbaum, which classifies all curve evolution equations. He then draws a complete parallel with another axiomatic approach using level-set methods: this leads to generalized curvature motions. Finally, novel, and very accurate, numerical schemes are proposed allowing one to compute the solution of highly degenerate evolution equations in a completely invariant way. The convergence of this scheme is also proved.

Take an apple and cut it into five pieces. Would you believe that these five pieces can be reassembled in such a manner that would to create two apples equal in shape and size to the original? Would you believe that you could make something as large as the Sun by breaking something so small as a pea into a finite number of pieces and putting it back together again? Neither did Leonard Wapner, author of "The Pea and the Sun", when he was first introduced to the Banach-Tarski paradox, which asserts exactly such a notion. Wapner writes in an engaging style that catalogues the people, events, and mathematics that contributed to the discovery of Banach and Tarski's magical paradox, making one of the most intriguing problems of advanced mathematics accessible to the non-mathematician.

John Stillwell’s Yearning for the Impossible is a new book that seeks to teach some mathematics to an audience of nonspecialists. Its title refers to the idea that mathematical advances tend to come about when researchers manage to understand ideas or constructions once thought to be impossible. So, for example, there are chapters about irrational numbers and imaginary numbers (after all, nobody used to think such things existed), chapters about 4-dimensional geometries and different orders of infinity (because nobody really knew whether one could make sense of such things), and a chapter about unique factorization via prime ideals (because unique factorization without prime ideals is, um, impossible).

Meant to serve an "entertaining textbook," this book belongs to a rare genre. It is written for all students and practitioners who deal with Fourier transformation. Fourier series as well as continuous and discrete Fourier transformation are covered, and particular emphasis is placed on window functions. Many illustrations and easy-to-solve exercises make the book especially accessible, and its humorous style will add to the pleasure of learning from it.

This Handbook deals with the foundations of incidence geometry, in relationship with division rings, rings, algebras, lattices, groups, topology, graphs, logic and its autonomous development from various viewpoints. Projective and affine geometry are covered in various ways. Major classes of rank 2 geometries such as generalized polygons and partial geometries are surveyed extensively.
More than half of the book is devoted to buildings at various levels of generality, including a detailed and original introduction to the subject, a broad study of characterizations in terms of points and lines, applications to algebraic groups, extensions to topological geometry, a survey of results on diagram geometries and nearby generalizations such as matroids.

To succeed in the practice of microelectronics in industry, students must develop the ability to think intuitively about circuits. They need to move beyond simply plugging and chugging numbers in equations and be prepared to face real design trade-offs.
Fundamentals of Microelectronics, Preview Edition helps students develop intuitive techniques so they can design and implement circuits not just analyze them. Using many real-word examples and applications, the text motivates the student to understand the importance of today's microelectronics.

Given the rapid software and hardware developments in DSP, it is vital for students to complement their theoretical learning with practical applications. Each chapter consists of a brief section on theory to explain the underlying mathematics and principles, a problem solving section, and a computer laboratory section with programming examples and exercises using MATLAB and Simulink. Applicable chapters include a hardware laboratory section composed of exercises using test and measuring equipment. This text offers a concise, easily understood presentation that makes the information accessible to students while building their proficiency with the software, the hardware, and the theory of DSP.

Content-Based Analysis Of Digital Video focuses on fundamental issues underlying the development of content access mechanisms for digital video. It treats topics that are critical to successfully automating the video content extraction and retrieval processes.

This book presents the theory and application of new methods of image compression based on self-transformations of an image. These methods lead to a representation of an image as a fractal, an object with detail at all scales. Very practical and completely up-to-date, this book will serve as a useful reference for those working in image processing and encoding and as a great introduction for those unfamiliar with fractals. The book begins with an elementary introduction to the concept of fractal image compression and contains a rigorous description of all the relevant mathematics of the subjects.

Possibly the most comprehensive overview of computer graphics as seen in the context of geometric modelling, this two volume work covers implementation and theory in a thorough and systematic fashion. Computer Graphics and Geometric Modelling: Mathematics, contains the mathematical background needed for the geometric modeling topics in computer graphics covered in the first volume. This volume begins with material from linear algebra and a discussion of the transformations in affine & projective geometry, followed by topics from advanced calculus & chapters on general topology, combinatorial topology, algebraic topology, differential topology, differential geometry, and finally algebraic geometry. Two important goals throughout were to explain the material thoroughly, and to make it self-contained. This volume by itself would make a good mathematics reference book, in particular for practitioners in the field of geometric modelling. Due to its broad coverage and emphasis on explanation it could be used as a text for introductory mathematics courses on some of the covered topics, such as topology (general, combinatorial, algebraic, and differential) and geometry (differential & algebraic).