Date Chapter.Section/Topics or Page/Problems T Jan 11 Lecture 1: Introduction: Vector Spaces Assignment 1 Due Tuesday January 25 Th 13 Lecture 2: Subspaces Assignment 2 Due Tuesday February 1 T 18 Lecture 3: More on sums of subspaces Linear Independence Th 20 Lecture 4: Linear Independence Assignment 3 Due Tuesday February 15 T 25 Lecture 5: Th 27 Lecture 6: T Feb 1 Lecture 7: Test for linear independence Size of spanning sets compared to size of linearly independent sets Assignment 4 Due Tuesday February 22 Th 3 Lecture 8: spanning sets and subspaces polynomials and proof by induction Basis for a vector space T 8 Lecture 9: Polynomials(?) Dimension Assignment 5 Due Tuesday March 1 Th 10 Lecture 10: Dimension and Linear Functions T 15 Lecture 11: Linear Functions (Group Activity) Th 17 Lecture 12: Linear Functions (Null Space and Range Space) Assignment 6 = Exam 2 Due Tuesday March 8 T 22 Lecture 13: Linear Functions (injective, surjective, and bijective) (pre-recorded Sunday February 20, 2022) Assignment 7 Due Tuesday March 22 Th 24 Lecture 14: Linear Functions and Matrices (pre-recorded Sunday February 20, 2022) T Mar 1 Lecture 15: Linear Functions and Invertibility Th 3 Lecture 16: More on invertibility T 8 Lecture 17: Quotient spaces Assignment 8 Due Tuesday March 29 Th 10 Lecture 18: Quotient spaces and product spaces T 15 Lecture 19: Dual spaces Assignment 9 Due Tuesday April 5 Assignment 10 Due Tuesday April 12 Th 17 Lecture 20: Duality T 22 spring break Th 24 spring break T 29 Lecture 21: Duality Th 31 Lecture 22: Duality (and Polynomials and Eigenvalues) T Apr 5 Lecture 23: Polynomials and Eigenvalues Assignment 11 Due Tuesday April 19 Th 7 Lecture 24: Duality summary and rank of a matrix Eigenvalues and Eigenvectors T 12 Lecture 25: Eigenvectors and diagonalization Conjugation Assignment 12 Due Tuesday April 26 Final Comments Final Assignment Due Tuesday April 28 Th 14 Lecture 26: Jordan Shear in the plane T 19 Lecture 27: More on Jordan Shear Matthew on Final Problem 41 Th 21 Lecture 28: T 26 Last lecture Th 28 T May 3 final exam 2:40-5:30