Hands-On Matrix Algebra Using R: Active and Motivated Learning with Applications

This is the first book of its kind which teaches matrix algebra, allowing the student to learn the material by actually working with matrix objects in modern computer environment of R. Instead of a calculator, R is a vastly more powerful free software and graphics system. The book provides a comprehensive overview of matrix theory without being bogged down in proofs or tedium. The reader can check each matrix result with numerical examples of exactly what they mean and understand their implications. The book does not shy away from advanced topics, especially the ones with practical applications. Contents: R Preliminaries Elementary Geometry and Algebra Using R Vector Spaces Matrix Basics and R Software Decision Applications: Payoff Matrix Determinant and Singularity of a Square Matrix The Norm, Rank and Trace of a Matrix Matrix Inverse and Solution of Linear Equations Eigenvalues and Eigenvectors Similar Matrices, Quadratic and Jordan Canonical Forms Hermitian, Normal and Positive Definite Matrices Kronecker Products and Singular Value Decomposition Simultaneous Reduction and Vec Stacking Vector and Matrix Differentiation Matrix Results for Statistics Generalized Inverse and Patterned Matrices Numerical Accuracy and QR Decomposition Readership: Undergraduates, high school teachers, researchers in mathematics, statistics and economics. Keywords: Mathematics; Statistics; Matrix Algebra