Chapter  demos 
1. Vectors 
Displacement along a Curve
2D Vector Addition
Vector Addition is Commutative
Dot Product
Normalizing Vectors
Vector Projection
From Vector to Line
From Vector to Plane
Normed Line
Cross Product of Vectors in the yz Plane

2. Systems of Linear Equations 
Linear Equations: Row and Column View
Planes, Solutions, and Gaussian Elimination of a 3x3 Linear System

3. Matrices 
Matrix Multiplication
LU Decomposition
3x3 Matrix Explorer
Linear Transformation Given by Images of Basis Vectors
Linear Transformations of a Polygon
Matrix Transformations: "F"
Matrix Transformation
Reflection Matrix in 2D
Vector Rotations in 3D
Combining Two 3D Rotations
Iterated Matrix Operations in 3D
Rotation Matrix Entries
Transition Matrices of Markov Chains
Adjacency Matrices of Manipulable Graphs

4. Eigenvalues and Eigenvectors 
3x3 Determinants Using Diagonals
3x3 Determinants by Expansion
Decomposition of a Vector in 2D
Determinants Seen Geometrically
The Determinant Using Traces
Tetrahedron Volume
Eigenvectors by Hand
Eigenvectors in 2D
Eigenvalue Problem for 2x2 Hermitian Matrices
Eigenvalue Plots of Certain Tridiagonal Matrices
Eigenvalues of Random Symmetric Matrices
Eigenvalues and Linear Phase Portraits
Network Centrality Using Eigenvectors
The Eigenvectors of a Random Graph

5. Orthogonality 
QR Decomposition
GramSchmidt Process in Two Dimensions
Numerical Instability in the GramSchmidt Algorithm

6. Vector Spaces 
Coordinates of a Point Relative to a Basis in 2D
Change of Basis in 2D

7. Distance and Approximation 
Singular Value Decomposition
Maximum Absolute Column Sum Norm
Maximum Absolute Row Sum Norm
Matrix Norm and Spectral Norm
Least Squares
Image Compression via the Singular Value Decomposition
