Matrix Algebra and Its Applications to Statistics and Econometrics

This book presents a unified treatment of the mechanics of mixtures of several constituents within the context of continuum mechanics, which takes into account the possibility of chemical reactions and interconversion of the constituents. After an introduction to the basic theory in the first few chapters, the book deals with a detailed exposition of the mechanics of a mixture of a fluid and an elastic solid, that is either isotropic or anisotropic and is capable of undergoing large deformations. Several boundary value and initial-boundary value problems are solved. The status of some special theories like those of Darcy and Biot are discussed. Such a study has relevance to several technologically significant problems in geomechanics, biomechanics, diffusion of contaminants and swelling and absorption of fluids in polymers and polymer composites, to mention a few Vector spaces; unitary and Euclidean spaces; linear transformations and matrices; some characteristics of matrices; factorization of matrices; operations on matrices; projectors and idempotent operators; generalized inverses; majorization; inequalities for Eigenvalues; matrix approximations; optimization problems in statistics and econometrics; quadratic subspaces; inequalities in statistics and econometrics; total least squares and regression