MATH 416: Abstract Linear Algebra
Spring 2021

Readings and problems are from Meckes & Meckes, Linear Algebra.
Starting with the second lecture, you are expected to watch the lecture before the class and answer a short quiz on Moodle.
You should also read the corresponding section of the textbook.
I recommend reading the advice for studying.
Midterms are March 1, March 29, April 26, see information about exams
Week Lecture Lecture Notes and Video Textbook sections Problems Due date
1 M 1/25 Introduction: Notes, Video Sec. 1.1 1.1.8, 1.1.10, 1.1.11 Feb 5
W 1/27 Gaussian Elimination: Notes, Video Sec. 1.2 1.2.4 (a,b,c), 1.2.6 (a,c,e), 1.2.10, 1.2.14
F 1/29 Geometry of Linear Systems: Notes, Video Sec. 1.3 1.3.4 (b,d,f), 1.3.6, 1.3.12
2 M 2/1 Fields: Notes, Video Sec. 1.4 1.4.1, 1.4.6, 1.4.8, 1.4.18 Feb 12
W 2/3 Vector Spaces: Notes, Video Sec. 1.5 1.5.2, 1.5.4, 1.5.10, 1.5.18
F 2/5 Linear Maps: Notes, Video Sec. 2.1 (until eigenvalues) 2.1.2, 2.1.4, 2.1.6
3 M 2/8 Eigenvectors: Notes, Video Sec. 2.1 (from eigenvalues)
Supplement
2.1.8, 2.1.10, 2.1.14, 2.1.16 Feb 19
W 2/10 Properties of Linear Maps: Notes, Video Sec 2.2 2.2.2, 2.2.4, 2.2.7, 2.2.14, 2.2.15
F 2/12 Matrix Multiplication: Notes, Video Sec. 2.3 2.3.2, 2.3.10, 2.3.11, 2.3.12 (a)
4 M 2/15 Elementary Matrices: Notes, Video Sec. 2.4 2.4.2, 2.4.4, 2.4.19, 2.4.22 Feb 26
W 2/17 No class
F 2/19 LU decomposition: Notes, Video Sec. 2.4 (again) 2.4.6, 2.4.8, 2.4.10, 2.4.16
6 M 2/22 Kernel and Range: Notes, Video Sec. 2.5 2.5.2, 2.5.4, 2.5.10, 2.5.11, 2.5.12 Mar 5
W 2/24 Error correcting codes: Notes, Video Sec. 2.6 2.5.6, 2.5.15, 2.5.16, 2.6.4, 2.6.8
F 2/26 No class
7 M 3/1 No class, First exam (takehome) Mar 12
W 3/3 Linear Independence: Notes, Video Sec. 3.1 3.1.2(a,b) 3.1.6, 3.1.8, 3.1.14
F 3/5 Bases: Notes, Video Sec. 3.2 3.2.2, 3.2.4 (b,d), 3.2.6 (b,d), 3.2.13
8 M 3/8 Bases and Linear Maps: Notes, Video Sec. 3.2 (again) 3.2.14, 3.2.16, 3.2.20 Mar 19
W 3/10 Dimension: Notes, Video Sec. 3.3 3.3.2(b,e), 3.3.8, 3.3.12, 3.3.22
F 3/12 Rank-Nullity Theorem: Notes, Video Sec. 3.4 3.4.2 (a,b,c), 3.4.4, 3.4.8, 3.4.14
9 M 3/15 Coordinates: Notes , Video Sec. 3.5 3.5.6 (a,b,c), 3.5.10, 3.5.12, 3.5.16, 3.5.18 Mar 26
W 3/17 Change of Basis: Notes, Video Sec. 3.6 3.6.2 (a,b), 3.6.4, 3.6.12
F 3/19 Similar Matrices: Notes , Video Sec. 3.6 (again) 3.6.10, 3.6.16, 3.6.18, 3.6.24, 3.6.26
10 M 3/22 Triangularization: Notes, Video Sec. 3.7 3.7.4, 3.7.10, 3.7.12, 3.7.14
(in 3.7.14: nonzero polynomial)
Apr 2
W 3/24 Holiday
F 3/26 Inner Products: Notes, Video Sec. 4.1 4.1.2, 4.1.6, 4.1.10, 4.1.12
(in 4.1.12(c): v2 is in W)
11 M 3/29 No class, Second exam (takehome) Apr 9
W 3/31 Cauchy-Schwarz Inequality: Notes, Video Sec. 4.1 (again) 4.1.4, 4.1.8, 4.1.14, 4.1.20
F 4/2 Orthonormal Bases: Notes , Video Sec. 4.2 4.2.4, 4.2.6, 4.2.8, 4.2.10, 4.2.18
12 M 4/5 Orthonormal Projections: Notes, Video Sec. 4.3 4.3.2(a,b), 4.3.4, 4.3.14, 4.3.22
(in 4.3.14(c): PW(A) = iIm(A))
Apr 16
W 4/7 Least Squares: Notes , Video Sec. 4.3 (again) 4.3.6, 4.3.8, 4.3.10, 4.3.18
F 4/9 Normed Spaces: Notes, Video Sec. 4.4 4.4.2, 4.4.4, 4.4.8, 4.4.11
13 M 4/12 Isometries: Notes , Video Sec. 4.5 4.4.16, 4.5.12, 4.5.16 Apr 23
W 4/14 QR Decomposition Notes , Video Sec. 4.5 (again) 4.5.4, 4.5.6, 4.5.8, 4.5.10, 4.5.14
F 4/16 Singular Values: Notes, Video Sec. 5.1 5.1.4, 5.1.6, 5.1.10, 5.1.14
14 M 4/19 Singular Value Decomposition: Notes , Video Sec. 5.2 5.2.2, 5.2.8, 5.2.16, 5.2.20 Apr 30
W 4/21 Adjoint Maps: Notes, Video Sec. 5.3 5.3.6, 5.3.8, 5.3.12, 5.3.18
F 4/23 Spectral Theorems: Notes, Video Sec. 5.4 5.4.2 (b,c), 5.4.6, 5.4.10, 5.4.22
15 M 4/26 No class, Third exam (takehome)
W 4/28 Determinants: Notes , Video Sec. 6.1 6.1.4, 6.1.6, 6.1.8, 6.1.10
F 4/30 Computing Determinants: Notes , Video Sec. 6.2 6.2.2 (b,c,d), 6.2.4, 6.2.6, 6.2.12
16 M 5/3 Characteristic Polynomial: Notes, Video Sec. 6.3 6.3.2, 6.3.4, 6.3.8, 6.3.18
(in 6.3.18: pA(x)=(-1)np(x))
Supplement Jordan Canonical Form: Notes, Video None
Supplement Linear Differential Equations: Notes, Video None
F 5/7 Final exam (takehome)