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; 2.1Introduction; 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 Matri