# Materials

• Lecture slides
• Lecture slides (2014,spring)
• Supplementary materials
• Old exams
• Homewotk solutions
• GNU Octave
• Mathematica Demonstrations
 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 y-z 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 Gram-Schmidt Process in Two Dimensions Numerical Instability in the Gram-Schmidt 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