Matrix algebra is one of the most important areas of mathematics for data analysis and for statistical theory. The first part of this book presents the relevant aspects of the theory of matrix algebra for applications in statistics. This part begins with the fundamental concepts of vectors and vector spaces, next covers the basic algebraic properties of matrices, then describes the analytic properties of vectors and matrices in the multivariate calculus, and finally discusses operations on matrices in solutions of linear systems and in eigenanalysis. This part is essentially...

Not only is matrix theory significant in a wide range of fields mathematical economics, quantum physics, geophysics, electrical network synthesis, crystallography, and structural engineering, among others-but with the vast proliferation of digital computers, knowledge of matrix theory is a must for every modern engineer, mathematician, and scientist. Matrices represent linear transformations from a finiteset of numbers to another finite set of numbers.
Since many important problems are linear, and since digital computers with finite memory manipulate only finite...

This text covers several aspects and solutions of the problems of linear vibrating systems with a finite number of degrees of freedom. It offers a detailed account of the part of the theory of matrices necessary for efficient problem-solving, beginning with a focus on developing the necessary tools in matrix theory in the first four chapters. The following chapters present numerical procedures for the relevant matrix formulations and the relevant theory of differential equations.
Directed toward a wide audience of applied mathematicians, scientists, and engineers, this book has much to...

Written for advanced undergraduate students, this highly regarded book presents an enormous amount of information in a concise and accessible format. Beginning with the assumption that the reader has never seen a matrix before, the authors go on to provide a survey of a substantial part of the field, including many areas of modern research interest.
Part One of the book covers not only the standard ideas of matrix theory, but ones, as the authors state, "that reflect our own prejudices," among them Kronecker products, compound and induced matrices, quadratic relations,...