(Ebook) Applied Matrix Algebra in the Statistical Sciences by Basilevsky, Alexander ISBN 9780486153377, 0486153371

(Ebook) Applied Matrix Algebra in the Statistical Sciences by Basilevsky, Alexander ISBN 9780486153377, 0486153371

DOVER BOOKS ON MATHEMATICS; Title Page; Copyright Page; Dedication; Table of Contents; Preface; Chapter 1 - Vectors; 1.1 Introduction; 1.2 Vector Operations; 1.3 Coordinates of a Vector; 1.4 The Inner Product of Two Vectors; 1.5 The Dimension of a Vector: Unit Vectors; 1.6 Direction Cosines; 1.7 The Centroid of Vectors; 1.8 Metric and Normed Spaces; 1.9 Statistical Applications; Chapter 2 - Vector Spaces; 2.1 Introduction; 2.2 Vector Spaces; 2.3 The Dimension of a Vector Space; 2.4 The Sum and Direct Sum of a Vector Space; 2.5 Orthogonal Basis Vectors.2.6 The Orthogonal Projection of a Vector2.7 Transformation of Coordinates; Chapter 3 - Matrices and Systems of Linear Equations; 3.1 Introduction; 3.2 General Types of Matrices; 3.3 Matrix Operations; 3.4 Matrix Scalar Functions; 3.5 Matrix Inversion; 3.6 Elementary Matrices and Matrix Equivalence; 3.7 Linear Transformations and Systems of Linear Equations; Chapter 4 - Matrices of Special Type; 4.1 Symmetric Matrices; 4.2 Skew-Symmetric Matrices; 4.3 Positive Definite Matrices and Quadratic Forms; 4.4 Differentiation Involving Vectors and Matrices; 4.5 Idempotent Matrices.4.6 Nilpotent Matrices4.7 Orthogonal Matrices; 4.8 Projection Matrices; 4.9 Partitioned Matrices; 4.10 Association Matrices; 4.11 Conclusion; Chapter 5 - Latent Roots and Latent Vectors; 5.1 Introduction; 5.2 General Properties of Latent Roots and Latent Vectors; 5.3 Latent Roots and Latent Vectors of Matrices of Special Type; 5.4 Left and Right Latent Vectors; 5.5 Simultaneous Decomposition of Two Symmetric Matrices; 5.6 Matrix Norms and Limits for Latent Roots; 5.7 Several Statistical Applications; Chapter 6 - Generalized Matrix Inverses; 6.1 Introduction; 6.2 Consistent Linear Equations.6.3 Inconsistent Linear Equations6.4 The Unique Generalized Inverse; 6.5 Statistical Applications; Chapter 7 - Nonnegative and Diagonally Dominant Matrices; 7.1 Introduction; 7.2 Nonnegative Matrices; 7.3 Graphs and Nonnegative Matrices; 7.4 Dominant Diagonal Matrices: Input-Output Analysis; 7.5 Statistical Applications; References; Index.This comprehensive text covers both applied and theoretical branches of matrix algebra in the statistical sciences. It also provides a bridge between linear algebra and statistical models. Appropriate for advanced undergraduate and graduate students, the self-contained treatment also constitutes a handy reference for researchers. The only mathematical background necessary is a sound knowledge of high school mathematics and a first course in statistics.Consisting of two interrelated parts, this volume begins with the basic structure of vectors and vector spaces. The latter part emphasizes the d.