Appendix A. List of Definitions
1 Linear Equations in Linear Algebra
Definition 1.1 A Single Linear Equation
Definition 1.2 Solution to a Linear System
Definition 1.11 Consistent
Definition 1.12 Row Equivalence
Definition 1.13 Echelon Form and Row Row Reduced Echelon Form
Definition 1.15 Pivot Position and Pivot Column
Definition 1.18 Pivot Variables and Free Variables
Definition 1.22 \(\mathbb{R}^n\)
Definition 1.26 Linear Combinations and Span
Definition 1.33 Matrix Vector Product as a Linear Combination
Definition 1.41 Homogeneous and inhomogeneous systems
Definition 1.44 Linear Independence and Dependence
Definition 1.49 Matrix Transformation
Definition 1.51 Linear Transformation
Definition 1.56 The Standard Vectors
Definition 1.60 Onto
Definition 1.62 One-to-One
2 Matrix Algebra
Definition 2.1 Zero Matrix
Definition 2.2 Identity Matrix
Definition 2.4 Matrix Product via Columns
Definition 2.9 Transpose
Definition 2.16 Invertible (Non-singular) Matrix
Definition 2.23 Elementary Matrix
Definition 2.35 Subset of \(\mathbb{R}^n\)
Definition 2.36 Subspace
Definition 2.41 Column Space and Null Space
Definition 2.45 Basis
Definition 2.50 Coordinates Relative to a Basis
Definition 2.53 Dimension
Definition 2.56 Rank
3 Determinants
Definition 3.1 Determinant
Definition 3.5 Cofactor
4 Vector Spaces
Definition 4.3 Markov Chain Definitions
Definition 4.5 Regular Stochastic Matrix
5 Eigenvectors and Eigenvalues
Definition 5.1 Eigenvector and Eigenvalue
Definition 5.4 Eigenspace
Definition 5.15 Charteristic Polynomial and Characteristic Equation
Definition 5.19 Algebraic Multiplicity
Definition 5.21 Geometric Multiplicity
Definition 5.27 Similarity
Definition 5.30 Diagonal Matrix
Definition 5.32 Diagonalizable Matrix
Definition 5.42 Complex Numbers
Definition 5.44 Complex Conjugate
Definition 5.45 Absolute Value (Modulus)
Definition 5.46 Polar Form of a Complex Number
6 Orthogonality and Least Squares
Definition 6.1 Dot Product
Definition 6.4 Length (Magnitude)
Definition 6.7 Unit Vector
Definition 6.8 Distance
Definition 6.10 Orthogonal Vectors
Definition 6.12 Orthogonal Complement
Definition 6.15 Row Space
Definition 6.20 Orthogonal Set
Definition 6.25 Orthogonal Projection
Definition 6.29 Orthonormal Basis
Definition 6.33 Orthogonal Matrix
Definition 6.40 Distance from a Subspace
Definition 6.50 Least Squares Solution
7 Google PageRank, Symmetric Matrices, and Quadratic Forms
Definition 7.12 Symmetric Matrix
Definition 7.23 Quadratic Form
Definition 7.28 Definiteness
