Linear Algebra
(spring 2018)
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syllabus
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Materials
Lecture slides
Lecture slides
(2017, spring)
Lecture slides (2014,spring)
Introduction
Chapter 1: Vectors
Chapter 2: Systems of Linear Equations
Chapter 3: Matrices
Chapter 4: Eigenvalues and Eigenvectors
Chapter 5: Orthogonality
Chapter 7: Distance and Approximation
Supplementary materials
Selected theorems
Theorems in Chapter 3,4,5 and 7.4
Diagram: matrix as a function
Old exams
Midterm exam (2010)
Midterm exam (2011)
Midterm exam (2012)
Midterm exam (2013)
Midterm exam (2014)
Midterm exam (2016)
Midterm exam (2017)
Final exam (2010)
Final exam (2011)
Final exam (2012)
Final exam (2013)
Final exam (2014)
Final exam (2016)
Final exam (2017)
Homewotk solutions
GNU Octave
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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