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.
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)