Notes and Reference
1 Systems of Linear Equations and Matrices
1.1 Introduction to Systems of Linear Equations
1.3 Matrices and Matrix Operations
1.4 Inverses; Algebraic Properties of Matrices
1.5 Elementary Matrices and a Method for Finding A−1
1.6 More on Linear Systems and Invertible Matrices
1.7 Diagonal, Triangular, and Symmetric Matrices
1.8 Introduction to Linear Transformations
1.9 Compositions of Matrix Transformations
2 Determinants
2.1 Determinants by Cofactor Expansion
3 Euclidean Vector Spaces
3.1 Vectors in 2-Space, 3-Space, and n-Space
3.2 Norm, Dot Product, and Distance in Rn
4 General Vector Spaces
5 Eigenvalues and Eigenvectors
6 Inner Product Spaces
6.2 Angle and Orthogonality in Inner Product Spaces
6.3 Gram-Schmidt Process; QR-Decomposition
6.4 Best Approximation; Least Squares
7 Diagonalization and Quadratic Forms
7.2 Orthogonal Diagonalization
8 General Linear Transformations
8.1 General Linear Transformations
8.2 Compositions and Inverse Transformations
9 Numerical Methods
9.3 Comparison of Procedures for Solving Linear Systems
10 Applications of Linear Algebra
10.1 Constructing Curves and Surfaces Through Specified Points
10.2 The Earliest Applications of Linear Algebra
10.3 Cubic Spline Interpolation
10.9 Equilibrium Temperature Distributions
10.15 Age-Specific Population Growth
10.16 Harvesting of Animal Populations