Introduction to Linear Algebra

Chapter 1 Systems of Linear Equations and Matrices 1 - 1.1 Systems of Linear Equations Exercise Set 1.1 - 1.2 Matrices and Elementary Row Operations Exercise Set 1.2 - 1.3 Matrix Algebra Exercise Set 1.3 - 1.4 The Inverse of a Square Matrix Exercise Set 1.4 - 1.5 Matrix Equations Exercise Set 1.5 - 1.6 Determinants Exercise Set 1.6 - 1.7 Elementary Matrices and LU Factorization Exercise Set 1.7 - 1.8 Applications of Systems of Linear Equatio Exercise Set 1.8 Review Exercises Chapter Test Chapter 2 Linear Combinations and Linear Independence - 2.1 Vectors in Rn Exercise Set 2.1 - 2.2 Linear Combinations Exercise Set 2.2 - 2.3 Linear Independence Exercise Set 2.3 Review Exercises Chapter Test Chapter 3 Vector Spaces - 3.1 Definition of a Vector Space Exercise Set 3.1 - 3.2 Subspaces Exercise Set 3.2 - 3.3 Basis and Dimension Exercise Set 3.3 - 3.4 Coordinates and Change of Basis Exercise Set 3.4 - 3.5 Application : Differential Equations Exercise Set 3.5 Review Exercises Chapter Test Chapter 4 Linear Transformations - 4.1 Linear Transformations Exercise Set 4.1 - 4.2 The Null Space and Range Exercise Set 4.2 - 4.3 Isomorphisms Exercise Set 4.3 - 4.4 Matrix Representation of a Linear Transformation Exercise Set 4.4 - 4.5 Similarity Exercise Set 4.5 - 4.6 Application : Computer Graphics Exercise Set 4.6 Review Exercises Chapter Test Chapter 5 Eigenvalues and Eigenvectors - 5.1 Eigenvalues and Eigenvectors Exercise Set 5.1 - 5.2 Diagonalization Exercise Set 5.2 - 5.3 Application : Systems of Linear Different Exercise Set 5.3 - 5.4 Application : Markov Chains Exercise Set 5.4 Review Exercises Chapter Test Chapter 6 Inner Product Spaces - 6.1 The Dot Product on Rn Exercise Set 6.1 - 6.2 Inner Product Spaces Exercise Set 6.2 - 6.3 Orthonormal Bases Exercise Set 6.3 - 6.4 Orthogonal Complements Exercise Set 6.4 - 6.5 Application : Least Squares Approximation Exercise Set 6.5 - 6.6 Diagonalization of Symmetric Matrices Exercise Set 6.6 - 6.7 Application : Quadratic Forms Exercise Set 6.7 - 6.8 Application : Singular Value Decomposition Exercise Set 6.8 Review Exercises Chapter Test A Preliminaries A.1 Algebra of Sets Exercise Set A.1 A.2 Functions Exercise Set A.2 A.3 Techniques of Proof Exercise Set A.3 A.4 Mathematical Induction Exercise Set A.4 Answers to Odd-Numbered Exercises A.3 Techniques of Proof Exercise Set A.3 A.4 Mathematical Induction Exercise Set A.4 Answers to Odd-Numbered Exercises