Systems of Linear Equations and Matrices |
Note: All relevant chapters end with Supplementary Exercises. |
Determinants |
Vectors in 2-Space and 3-Space / 1: |
Linear Equations and Matrices |
Euclidean Vector Spaces |
Systems of Linear Equations |
General Vector Spaces |
Matrices |
Inner Product Spaces |
Matrix Multiplication |
Eigenvalues, Eigenvectors |
Algebraic Properties of Matrix Operations |
Linear Transformations |
Special Types of Matrices and Partitioned Matrices |
Additional Topics |
Matrix Transformations |
Complex Vector Spaces |
Computer Graphics |
Answers to Exercises |
Correlation Coefficient (Optional) |
Photo Credits |
Index / 2: |
Solving Linear Systems |
Echelon Form of a Matrix |
Elementary Matrices: Finding A-1 |
Equivalent Matrices |
LU-Factorization (Optional) |
Real Vector Spaces / 3: |
Vectors in the Plane and in 3-space |
Vector Spaces |
Subspaces |
Span and Linear Independence |
Basis and Dimension |
Homogeneous Systems |
Coordinates and Isomorphisms |
Rank of a Matrix |
Standard Inner Product on R2 and R3 / 4: |
Cross Product in R3 (Optional) |
Gram-Schmidt Process |
Orthogonal Complements |
Least Squares (Optional) |
Linear Transformations and Matrices / 5: |
Definition and Examples |
Kernel and Range of a Linear Transformation |
Matrix of a Linear Transformation |
Vector Space of Matrices and Vector Space of Linear Transformations (Optional) |
Similarity |
Inroduction to Homogeneous Coordinates (Optional) |
Definition / 6: |
Properties of Determinants |
Cofactor Expansion |
Inverse of a Matrix |
Other Applications of Determinants |
Determinants from a Computational Point of View |
Eigenvalues and Eigenvectors / 7: |
Diagonalization and Similar Matrices |
Stable Age Distribution in a Population |
Markov Processes (Optional) |
Diagonalization of Symmetric Matrices |
Spectral Decomposition and Singular Value Decomposition (Optional) |
Real Quadratic Forms |
Conic Sections |
Quadric Surfaces |
Dominant Eigenvalue and Principal Component Analysis (Optional) |
Differential Equations (Optional) / 8: |
Differential Equations |
Dynamical Systems |
MATLAB for Linear Algebra / 9: |
Input and Output in MATLAB |
Matrix Operations in MATLAB |
Matrix Powers and Some Special Matrices |
Elementary Row Operations in MATLAB |
Matrix Inverses in MATLAB |
Vectors in MATLAB |
Applications of Linear Combinations in MATLAB |
Linear Transformations in MATLAB |
MATLAB Command Summary |
MATLAB Exercises / 10: |
Preliminaries Sets Functions / Appendix A: |
Complex Numbers Complex Numbers Complex Numbers in Linear Algebra / Appendix B: |
Introduction to Proofs / Appendix C: |
Answers to Odd-Numbered Exercises |
Systems of Linear Equations and Matrices |
Note: All relevant chapters end with Supplementary Exercises. |
Determinants |