Preface Part I Introduction: Three Examples Chapter 1. SYSTEMS OF LINEAR ALGEBRAIC EQUATIONS 1.1 Linear Algebraic Equations 1.2 Matrix Representation of Linear Systems and the GaussÂ]Jordan Algorithm 1.3 The Complete Gauss Elimination Algorithm 1.4 Echelon Form and Rank 1.5 Computational Considerations Chapter 2. MATRIX ALGEBRA 2.
1 Matrix Multiplication 2.2 Some Applications of Matrix Operators 2.3 The Inverse and the Transpose 2.4 Determinants 2.5 Three Important Determinant Rules Review Problems for Part I Technical Writing Exercises for Part I Group Projects for Part I A. LU Factorization B. TwoÂ]Point Boundary Value Problems C. Electrostatic Voltage D.
Kirchhoff's Laws E. Global Positioning Systems Part II Introduction: The Structure of General Solutions to Linear Algebraic Equations Chapter 3. VECTOR SPACES 3.1 General Spaces, Subspaces, and Spans 3.2 Linear Dependence 3.3 Bases, Dimension, and Rank Chapter 4. ORTHOGONALITY 4.1 Orthogonal Vectors and the GramÂ]Schmidt Algorithm Norm 4.
2 Orthogonal Matrices 4.3 Least Squares 4.4 Function Spaces Review Problems for Part II Magic square Controllability Technical Writing Exercises for Part II Group Projects for Part II A. Orthogonal Matrices, Rotations, and Reflections B. Householder Reflectors and the QR Factorization C. Infinite Dimensional Matrices Part III Introduction: Reflect on This Chapter 5. Eigenvalues and Eigenvectors 5.1 Eigenvector Basics 5.
2 Calculating Eigenvalues and Eigenvectors 5.3 Symmetric and Hermitian Matrices Chapter 5. Summary Chapter 6. Similarity 6.1 Similarity Transformations and Diagonalizability 6.2 Principal Axes Normal Modes 6.3 Schur Decomposition and Its Implications 6.4 The Power Method and the QR Algorithm Chapter 7.
Linear Systems of Differential Equations 7.1 First Order Linear Systems of Differential Equations 7.2 The Matrix Exponential Function 7.3 The Jordan Normal Form Review Problems for Part III Technical Writing Exercises for Part III Group Projects for Part III A. Positive Definite Matrices B. Hessenberg Form C. The Discrete Fourier Transform and Circulant Matrices Answers to OddÂ]Numbered Problems Index.