Product Description: This concise introduction to the methods and techniques of vector analysis is suitable for college undergraduates in mathematics as well as students of physics and engineering. Rich in exercises and examples, the straightforward presentation focuses on physical ideas rather than mathematical rigor...read more

A traditional approach to developing multivariate statistical theory is algebraic. Sets of observations are represented by matrices, linear combinations are formed from these matrices by multiplying them by coefficient matrices, and useful statistics are found by imposing various criteria of optimization on these combinations. Matrix algebra is the vehicle for these calculations. A second approach is computational. Since many users find that they do not need to know the mathematical basis of the techniques as long as they have a way to transform data into results, the computation can be done by a package of computer programs that somebody else has written. An approach from this perspective emphasizes how the computer packages are used, and is usually coupled with rules that allow one to extract the most important numbers from the output and interpret them. Useful as both approaches are--particularly when combined--they can overlook an important aspect of multivariate analysis. To apply it correctly, one needs a way to conceptualize the multivariate relationships that exist among variables. This book is designed to help the reader develop a way of thinking about multivariate statistics, as well as to understand in a broader and more intuitive sense what the procedures do and how their results are interpreted. Presenting important procedures of multivariate statistical theory geometrically, the author hopes that this emphasis on the geometry will give the reader a coherent picture into which all the multivariate techniques fit.

Product Description: "A handy book like this," noted The Mathematical Gazette, "will fill a great want." Devoted to fully worked out examples, this unique text constitutes a self-contained introductory course in vector analysis for undergraduate and graduate students of applied mathematics...read more

This book presents the reader with new operators and matrices that arise in the area of matrix calculus. The properties of these mathematical concepts are investigated and linked with zero-one matrices such as the commutation matrix. Elimination and duplication matrices are revisited and partitioned into submatrices. Studying the properties of these submatrices facilitates achieving new results for the original matrices themselves. Different concepts of matrix derivatives are presented and transformation principles linking these concepts are obtained. One of these concepts is used to derive new matrix calculus results, some involving the new operators and others the derivatives of the operators themselves. The last chapter contains applications of matrix calculus, including optimization, differentiation of log-likelihood functions, iterative interpretations of maximum likelihood estimators, and a Lagrangian multiplier test for endogeneity.

Product Description: There exists a vast literature on numerical methods of linear algebra. In our bibliography list, which is by far not complete, we included some monographs on the subject [46], [15], [32], [39], [11], [21]. The present book is devoted to the theory of algorithms for a single problem of linear algebra, namely, for the problem of solving systems of linear equations with non-full-rank matrix of coefficients...read more

Product Description: We always come cross several decision-making problems in our daily life. Such problems are always conflicting in which many different view points should be satisfied. In politics, business, industrial systems, management science, networks, etc...read more

Product Description: This book is intended as a self-study text for students following courses in science and engineering where vectors are used. The material covered and the level of treatment should be sufficient to provide the vector algebra and vector calculus skills required for most honours courses in mechanics, electromagnetism, fluid mechanics, aerodynamics, applied mathematics and mathematical modelling...read more

Product Description: This brief undergraduate-level text by a prominent Cambridge-educated mathematician explores the relationship between algebra and geometry. An elementary course in plane geometry is the sole requirement for Gilbert de B. Robinson's text, which is the result of several years of teaching and learning the most effective methods from discussions with students...read more

Product Description: The theory of Vector Optimization is developed by a systematic usage of infimum and supremum. In order to get existence and appropriate properties of the infimum, the image space of the vector optimization problem is embedded into a larger space, which is a subset of the power set, in fact, the space of self-infimal sets...read more

The first eight chapters of this book were originally published in 1966 as the successful Introduction to Elementary Vector Analysis. In 1970, the text was considerably expanded to include six new chapters covering additional techniques (the vector product and the triple products) and applications in pure and applied mathematics. It is that version which is reproduced here. The book provides a valuable introduction to vectors for teachers and students of mathematics, science and engineering in sixth forms, technical colleges, colleges of education and universities.

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Product Description: Writing a new book on the classic subject of Special Relativity, on which numerous important physicists have contributed and many books have already been written, can be like adding another epicycle to the Ptolemaic cosmology. Furthermore, it is our belief that if a book has no new elements, but simply repeats what is written in the existing literature, perhaps with a different style, then this is not enough to justify its publication...read more

Product Description: Methods used for regional development analysis are employed mainly to make forecasts and comparisons. Forecasting models of various types (e.g. econometric models) are usually used for forecasting. Recently, vector-autoregressive models (VAR) have become popular...read more

Product Description: Dealing primarily with the development of vector algebra as a mathematical tool in geometry, this elementary text features applications to trigonometry, both plane and spherical, and algebra. Appropriate for high school students and college undergraduates, it offers greater insights into theorems by employing vector and analytic proofs, rather than synthetic proofs...read more