Week 1: 8/28 
Introduction 
Joe's Notes
Demo: Best fit ellipse
Demo: Rabbit population
Demo: A Plane
Demo: Two Planes

Homework #1
Due 9/6 11:59pm
Note: HW#1 also covers the recorded lecture.

Vectors and Matrices (Ch. 1, 2.4, 2.7)

Joe's Notes
Recorded: Watch on WarpWire (on Sakai) before the second lecture.

Solving Equations: Elimination (2.2) 
Joe's Notes

Problem Session 

Week 2: 9/4 
Gauss–Jordan Algorithm (2.2, 2.5) 
Joe's Notes
Gauss–Jordan Slideshow
Rabinoff's Reliable Row Reducer

Homework #2
Due 9/13 11:59pm

LU Decomposition (2.3, 2.6) 
Joe's Notes

Problem Session 
Quiz

Week 3: 9/11 
Parametric Form 
Joe's Notes
Demo: Parameterized Line
Demo: Parameterized Plane

Homework #3
Due 9/20 11:59pm

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 R^{2}
Demo: Linear combinations of two vectors in R^{3}
Demo: Linear combinations of three vectors in R^{3}
Demo: Span of 1 vector in R^{2}
Demo: Span of 2 vectors in R^{2}
Demo: Span of 1 vector in R^{3}
Demo: Span of 2 vectors in R^{3}
Demo: Span of 3 vectors in R^{3}
Demo: Column Picture for Consistency: Consistent
Demo: Column Picture for Consistency: Inconsistent
Demo: Row/column picture: parallel lines
Demo: Row/column picture: sometimes inconsistent

Problem Session 
Quiz

Week 4: 9/18 
Subspaces (3.1, 3.2) 
Joe's Notes
Demo: Column and Null Space

Homework #4
Due 9/27 11:59pm

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 R^{2}

Problem Session 
Quiz

Week 5: 9/25 
Fundamental Subspaces (3.4, 3.5) 
Joe's Notes
Demo: Ranknullity: n=3, r=0
Demo: Ranknullity: n=3, r=1
Demo: Ranknullity: n=3, r=2
Demo: Ranknullity: n=3, r=3

Homework #5
Due 10/4 11:59pm

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 R^{2}

Problem Session 

Week 6: 10/2 
Orthogonal Projections (4.2) 
Joe's Notes
Demo: Decomposition relative a line in R^{2}
Demo: Decomposition relative a line in R^{3}
Demo: Decomposition relative a plane in R^{3}
Demo: Projection onto a plane
Demo: Projection onto a line
Demo: Projection onto a plane

Homework #6
Due 10/11 11:59pm

Projection Matrices (4.2) 
Joe's Notes

Friday, 10/6: MIDTERM 1 
Practice Midterm
and Solutions
Midterm
and Solutions

Week 7: 10/9 
Least Squares (4.3) 
Joe's Notes
Demo: LeastSquares
Demo: Bestfit line
Demo: Bestfit parabola
Demo: Bestfit trigonometric function
Demo: Bestfit ellipse
Demo: Bestfit ellipse: what is minimized?

Homework #7
Due 10/19 11:59pm

Gram–Schmidt and QR (4.4) 
Joe's Notes
Demo: Projection formula

Problem Session 

Week 8: 10/16 
FALL BREAK

Homework #8
Due 10/25 11:59pm

Determinants I (5.1, 5.3) 
Joe's Notes

Problem Session 

Week 9: 10/23 
Determinants II (5.2) 
Joe's Notes
Supplement: cofactor matrix

Homework #9
Due 11/1 11:59pm

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

Problem Session 

Week 10: 10/30 
Diagonalization: Vector Form (6.2) 
Joe's Notes

Homework #10
Due 11/8 11:59pm

Diagonalization: Geometry (6.2) 
Joe's Notes
Dynamics demos:

Problem Session 

Week 11: 11/6 
Complex Numbers; Euler's Formula (9.1)

Joe's Notes
Recorded: Watch on WarpWire (on Sakai) before Tuesday's lecture.

Homework #11
Due 11/15 11:59pm

AM/GM and Diagonalizability (6.2) 
Joe's Notes
Supplement: Proof of the AM≥GM theorem
AM/GM demos:
Dynamics with a Complex Eigenvalue

Systems of ODEs (6.3) 
Joe's Notes

Friday, 11/10: MIDTERM 2 
Practice Midterm
and Solutions
Midterm
and Solutions

Week 12: 11/13 
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

Homework #12
Due 11/22 11:59pm

LDL^{T}; Quadratic Optimization (2.7, 6.5) 
Joe's Notes
Supplement: LDL^{T} and Cholesky

Problem Session 

Week 13: 11/20 
Quadratic Optimization II (6.5) 
Joe's Notes

Homework #13
Due 11/29 11:59pm

THANKSGIVING

Week 14: 11/27 
SVD: Outer Product Form (7.1, 7.2) 
Joe's Notes

Homework #14
Due 12/6 11:59pm

SVD: Matrix Form (7.3) 
Joe's Notes

Problem Session 

Week 15: 12/4 
PCA I (7.3, 7.4) 
Joe's Notes

Homework #15
(Not collected)

PCA II (7.3) 
Joe's Notes

Problem Session 


Final exams:
218D1 (001):  Friday, 12/15, 2–5pm 
218D1 (002):  Friday, 12/15, 7–10pm 

Practice Final
and Solutions
