Basilevsky Alexander. Applied Matrix Algebra in the Statistical Sciences

Dover Publications, 2005. — 722 p.In recent decades matrix algebra and statistics and probability have become two of the most important areas of theoretical and applied mathematics, in terms of university curricula as well as actual research in the social, geographical, human, and life sciences. With a growing awareness of the usefulness of matrices in the statistical sciences has come a very elegant development of statistical theory, combining the principles of probability and linear algebra. This has greatly increased our understanding of the algebraic linear structures and properties of statistical models. At the same time, however, many of the more specialized theorems of linear algebra, as well as particular types of matrices commonly used in statistics, are usually not discussed in the more theoretical linear algebra texts, whose main purpose is to give the student a broad perspective of linear algebraic structures rather than a more specialized view. Usually matrix results of interest to statisticians are scattered in the appendices and introductory chapters of advanced statistical publications or are discussed in journal articles not readily available to the student and researcher. This in turn tends to influence university programs in statistics to place less importance on matrix algebra than it deserves, with the result that students involved in statistics and other quantitative programs are often forced to rely on courses taught in pure mathematics in order to obtain even the most elementary notions of applied linear algebra.