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Topic and Section |
Materials |
Homework |
Week 1: 8/26 |
Introduction |
Joe's Notes
Demo: Best fit ellipse
Demo: Rabbit population
Demo: A Plane
Demo: Two Planes
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Homework #1
Due 9/4 11:59pm
Solutions
Note: HW#1 also covers the recorded lecture.
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Vectors and Matrices (Ch. 1, 2.4, 2.7)
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Joe's Notes
Recorded: Watch on WarpWire (on Canvas) before the second lecture.
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Solving Equations: Elimination (2.2) |
Joe's Notes
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Problem Session |
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Week 2: 9/2 |
Gauss–Jordan Algorithm (2.2, 2.5) |
Joe's Notes
Gauss–Jordan Slideshow
Rabinoff's Reliable Row Reducer
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Homework #2
Due 9/11 11:59pm
Solutions
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LU Decomposition (2.3, 2.6) |
Joe's Notes
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Problem Session |
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Week 3: 9/9 |
Parametric Form |
Joe's Notes
Demo: Parameterized Line
Demo: Parameterized Plane
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Homework #3
Due 9/18 11:59pm
Solutions
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Spans (3.2, 3.3) |
Joe's Notes
Demo: A vector
Demo: Scalar multiplication
Demo: Vector addition
Demo: Vector subtraction
Demo: Linear combinations of two vectors in R2
Demo: Linear combinations of two vectors in R3
Demo: Linear combinations of three vectors in R3
Demo: Span of 1 vector in R2
Demo: Span of 2 vectors in R2
Demo: Span of 1 vector in R3
Demo: Span of 2 vectors in R3
Demo: Span of 3 vectors in R3
Demo: Column Picture for Consistency: Consistent
Demo: Column Picture for Consistency: Inconsistent
Demo: Row/column picture: parallel lines
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Problem Session |
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Week 4: 9/16 |
Subspaces (3.1, 3.2) |
Joe's Notes
Demo: Column and Null Space
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Homework #4
Due 9/25 11:59pm
Solutions
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Linear Independence and Basis (3.4, 3.5) |
Joe's Notes
Demo: Coplanar vectors
Demo: Redundant parameterization
Demo: Linearly dependent vectors
Demo: Linearly independent vectors
Demo: Linear (In)dependence of 1 vector
Demo: Linear (In)dependence of 2 vectors
Demo: Linear (In)dependence of 3 vectors
Demo: Linear Dependence of 3 vectors in R2
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Problem Session |
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Week 5: 9/23 |
Fundamental Subspaces (3.4, 3.5) |
Joe's Notes
Demo: Rank-nullity: n=3, r=0
Demo: Rank-nullity: n=3, r=1
Demo: Rank-nullity: n=3, r=2
Demo: Rank-nullity: n=3, r=3
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Homework #5
Due 10/2 11:59pm
Solutions
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Orthogonal Complements (3.5, 4.1) |
Joe's Notes
Demo: Closest vector to b
Demo: Orthogonal complement of one vector
Demo: Orthogonal complement of two vectors
Demo: Orthogonal complements in R2
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Problem Session |
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Week 6: 9/30 |
Orthogonal Projections (4.2) |
Joe's Notes
Demo: Decomposition relative a line in R2
Demo: Decomposition relative a line in R3
Demo: Decomposition relative a plane in R3
Demo: Projection onto a plane
Demo: Projection onto a line
Demo: Projection onto a plane
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Homework #6
Due 10/9 11:59pm
Solutions
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Projection Matrices (4.2) |
Joe's Notes
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Friday, 10/4: MIDTERM 1 |
Practice Midterm
and Solutions
Midterm
and Solutions
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Week 7: 10/7 |
Least Squares (4.3) |
Joe's Notes
Demo: Least-Squares
Demo: Best-fit line
Demo: Best-fit parabola
Demo: Best-fit trigonometric function
Demo: Best-fit ellipse
Demo: Best-fit ellipse: what is minimized?
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Homework #7
Due 10/16 11:59pm
Solutions
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Gram–Schmidt and QR (4.4) |
Joe's Notes
Demo: Projection formula
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Problem Session |
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Week 8: 10/14 |
FALL BREAK
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Homework #8
Due 10/23 11:59pm
Solutions
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Determinants I (5.1, 5.3) |
Joe's Notes
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Problem Session |
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Week 9: 10/21 |
Determinants II (5.2) |
Joe's Notes
Supplement: cofactor matrix
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Homework #9
Due 10/30 11:59pm
Solutions
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Eigenvalues and Eigenvectors (6.1) |
Joe's Notes
Demo: Rabbits Multiply
Demo: Eigenspaces of a flip
Demo: Eigenspaces of a shear
Demo: Eigenspaces of a rotation
Demo: Eigenspaces of the rabbit matrix
Demo: Eigenspaces of a 3x3 matrix
Demo: Eigenspaces of a projection matrix
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Problem Session |
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Week 10: 10/28 |
Diagonalization: Vector Form (6.2) |
Joe's Notes
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Homework #10
Due 11/6 11:59pm
Solutions
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Diagonalization: Geometry (6.2) |
Joe's Notes
Dynamics demos:
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Problem Session |
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Week 11: 11/4 |
Complex Numbers; Euler's Formula (9.1)
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Joe's Notes
Recorded: Watch on WarpWire (on Canvas) before Tuesday's lecture.
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Homework #11
Due 11/13 11:59pm
Solutions
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AM/GM and Diagonalizability (6.2) |
Joe's Notes
Supplement: Proof of the AM≥GM theorem
AM/GM demos:
Dynamics with a Complex Eigenvalue
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Stochastic Processes and PageRank |
Joe's Notes
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Friday, 11/8: MIDTERM 2 |
Practice Midterm
and Solutions
Midterm
and Solutions
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Week 12: 11/11 |
Spectral Theorem (6.4) |
Joe's Notes
Demo: Eigenspaces of a 3x3 symmetric matrix
Demo: Eigenspaces of a 3x3 symmetric matrix (GM=2)
Demo: Dynamics of a 2x2 symmetric matrix
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Homework #12
Due 11/20 11:59pm
Solutions
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LDLT; Quadratic Optimization (2.7, 6.5) |
Joe's Notes
Supplement: LDLT and Cholesky
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Problem Session |
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Week 13: 11/18 |
Quadratic Optimization II (6.5) |
Joe's Notes
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Homework #13
Due 11/27 11:59pm
Solutions
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SVD: Outer Product Form (7.1, 7.2) |
Joe's Notes
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Problem Session |
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Week 14: 11/25 |
SVD: Matrix Form (7.3) |
Joe's Notes
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Homework #14
Due 12/6 11:59pm
Solutions
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THANKSGIVING
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Week 15: 12/2 |
PCA I (7.3, 7.4) |
Joe's Notes
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Homework #15
(Not collected)
Solutions
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PCA II (7.3) |
Joe's Notes
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Problem Session |
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Final exams:
218D-1 (001): | Thursday, 12/12, 9am–noon |
218D-1 (002): | Monday, 12/16, 2–5pm |
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Practice Final
and Solutions
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