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Full Description
Poole's "Linear Algebra: A Modern Introduction, Cengage International Edition", 5th, emphasizes a vectors approach and prepares students to transition from computational to theoretical mathematics. Balancing theory and applications, the conversational writing style combines traditional presentation with student-centered learning. Theoretical, computational, and applied topics are presented in a flexible, integrated way. Stressing geometric understanding before computational techniques, vectors and vector geometry are introduced early to help students visualize concepts and develop mathematical maturity for abstract thinking. Applications drawn from a variety of disciplines reinforce linear algebra as a valuable tool for modeling real-life problems. Exercises allow students to practice linear algebra concepts and techniques. Learning objectives in each section serve as a guide for students and instructors.
Contents
Chapter 1: Vectors
Introduction: The Racetrack Game. The Geometry and Algebra of Vectors. Length and Angle: The Dot Product. Lines and Planes. Applications. Chapter Review.
Chapter 2: Systems of Linear Equations
Introduction: Triviality. Introduction to Systems of Linear Equations. Direct Methods for Solving Linear Systems. Spanning Sets and Linear Independence. Applications. Iterative Methods for Solving Linear Systems. Chapter Review.
Chapter 3: Matrices
Introduction: Matrices in Action. Matrix Operations. Matrix Algebra. The Inverse of a Matrix. The LU Factorization. Subspaces, Basis, Dimension, and Rank. Introduction to Linear Transformations. Applications. Chapter Review.
Chapter 4: Eigenvalues and Eigenvectors
Introduction: A Dynamical System on Graphs. Introduction to Eigenvalues and Eigenvectors. Determinants. Eigenvalues and Eigenvectors of n x n Matrices. Similarity and Diagonalization. Iterative Methods for Computing Eigenvalues. Applications and the Perron-Frobenius Theorem. Chapter Review
Chapter 5: Orthogonality
Introduction: Shadows on a Wall. Orthogonality in Rn. Orthogonal Complements and Orthogonal Projections. The Gram-Schmidt Process and the QR Factorization. Orthogonal Diagonalization of Symmetric Matrices. Applications. Chapter Review.
Chapter 6: Vector Spaces
Introduction: Fibonacci in (Vector) Space. Vector Spaces and Subspaces. Linear Independence, Basis, and Dimension. Change of Basis. Linear Transformations. The Kernel and Range of a Linear Transformation. The Matrix of a Linear Transformation. Applications. Chapter Review.
Chapter 7: Distance and Approximation
Introduction: Taxicab Geometry. Inner Product Spaces. Norms and Distance Functions. Least Squares Approximation. The Singular Value Decomposition. Applications. Chapter Review.
Chapter 8: Codes
Introduction: ASCII. Code Vectors. Error-Correcting Codes. Dual Codes. Linear Codes. The Minimum Distance of a Code. Chapter Review.
Chapter A: Appendices
Mathematical Notation and Methods of Proof. Mathematical Induction. Complex Numbers. Polynomials. Technology Bytes.
