Fundamentals of Matrix Analysis with Applications

PART I: INTRODUCTION: THREE EXAMPLES 1. Systems of Linear Algebraic Equations 2. Matrix Algebra PART II: INTRODUCTION: THE STRUCTURE OF GENERAL SOLUTIONS TO LINEAR ALGEBRAIC EQUATIONS 3. Vector Spaces 4. Orthogonality PART III: INTRODUCTION: REFLECT ON THIS 5. Eigenvectors and Eigenvalues 6. Similarity 7. Linear Systems of Differential Equations An accessible and clear introduction to linear algebra with a focus on matrices and engineering applications Providing comprehensive coverage of matrix theory from a geometric and physical perspective, Fundamentals of Matrix Analysis with Applications describes the functionality of matrices and their ability to quantify and analyze many practical applications. Written by a highly qualified author team, the book presents tools for matrix analysis and is illustrated with extensive examples and software implementations. Beginning with a detailed exposition and review of the Gauss elimination method, the authors maintain readers' interest with refreshing discussions regarding the issues of operation counts, computer speed and precision, complex arithmetic formulations, parameterization of solutions, and the logical traps that dictate strict adherence to Gauss's instructions. The book heralds matrix formulation both as notational shorthand and as a quantifier of physical operations such as rotations, projections, reflections, and the Gauss reductions. Inverses and eigenvectors are visualized first in an operator context before being addressed computationally. Least squares theory is expounded in all its manifestations including optimization, orthogonality, computational accuracy, and even function theory.…