MATH 416: Abstract Linear Algebra
Spring 2019

Readings and problems are from Meckes & Meckes.
You are expected to attend every class and to read from the book before class. I recommend reading the advice for studying.
Remark/warning: Schedule and homeworks corresponding to future lectures are tentative
Midterms are Feb 11, Mar 4, April 15 at 7pm, see information about exams
Week Lecture Lecture Notes Reading for next time Problems Due date
1 M 1/14 Introduction Sec. 1.1, 1.2 Read this and do the exercise for practice proof 1.
From the book: 1.1.5, 1.1.8, 1.1.10, 1.1.11
Jan 25
W 1/16 Gaussian Elimination Sec. 1.3 1.2.4 (a,b,c), 1.2.6, 1.2.10, 1.2.14
F 1/18 Geometry of Linear Systems Sec. 1.4 1.3.4, 1.3.6, 1.3.9, 1.3.12
2 M 1/21 MLK Jr Day Feb 1
W 1/23 Fields Sec. 1.5 1.4.1, 1.4.6, 1.4.8, 1.4.16, 1.4.18
F 1/25 Vector Spaces Sec. 2.1 1.5.2, 1.5.4, 1.5.10, 1.5.18, 1.5.20
3 M 1/28 Linear Maps Sec. 2.1 (again) 2.1.2, 2.1.4, 2.1.5, 2.1.6 Feb 15
W 1/30 Too cold for class
F 2/1 Eigenvectors Sec. 2.2 2.1.8, 2.1.10, 2.1.12, 2.1.14, 2.1.16
M 2/4 No class this week
to make up for
evening midterms
W 2/6
F 2/8
4 M 2/11 Properties of Linear Maps Sec 2.3 2.2.2, 2.2.4, 2.2.7, 2.2.14, 2.2.15 Feb 22
W 2/13 Matrix Multiplication Sec. 2.4 2.3.2, 2.3.8, 2.3.10, 2.3.11, 2.3.12 (a)
F 2/15 Elementary Matrices Sec. 2.4 (again) 2.4.2, 2.4.4, 2.4.19, 2.4.22
5 M 2/18 LU decomposition Sec. 2.5 2.4.6, 2.4.8, 2.4.10, 2.4.16 Mar 1
W 2/20 Kernel and Range Sec. 2.6 2.5.2, 2.5.4, 2.5.10, 2.5.11, 2.5.12
F 2/22 Error correcting codes Sec. 3.1 2.5.6, 2.5.15, 2.5.16, 2.6.4, 2.6.8
6 M 2/25 Linear Independence Sec. 3.2 3.1.2(a,b) 3.1.6, 3.1.8, 3.1.9, 3.1.14 Mar 8
W 2/27 Bases Sec. 3.3 3.2.2, 3.2.4 (b,d), 3.2.6 (b,d), 3.2.13
F 3/1 Bases and Linear Maps Sec. 3.3 (again) 3.2.14, 3.2.16, 3.2.20, 3.3.2(b,e)
7 M 3/4 Dimension Sec. 3.4 3.3.8, 3.3.9, 3.3.12, 3.3.22 Mar 15
W 3/6 Rank-Nullity Theorem Sec. 3.5 3.4.2 (a,b,c), 3.4.3, 3.4.4, 3.4.8, 3.4.9
F 3/8 Coordinates Sec. 3.6 3.5.6 (a,b,c), 3.5.10, 3.5.12, 3.5.18
8 M 3/11 Change of Basis Sec. 3.6 (again) 3.5.11, 3.5.16, 3.6.2 (a,b), 3.6.4, 3.6.12 Mar 29
W 3/13 Similar Matrices Sec. 3.7 3.6.10, 3.6.16, 3.6.18, 3.6.20, 3.6.23
F 3/15 Triangularization Sec. 6.1 3.7.4, 3.7.7, 3.7.10, 3.7.12, 3.7.14
(in 3.7.14: nonzero polynomial)
9 M 3/25 Determinants Sec. 6.2 6.1.4, 6.1.6, 6.1.8, 6.1.10 Apr 5
W 3/27 Computing Determinants Sec. 6.3 6.2.2 (b,c,d), 6.2.9, 6.2.12, 6.2.13
F 3/29 Characteristic Polynomial Sec. 4.1 6.3.1, 6.3.3, 6.3.4, 6.3.7, 6.3.18
(in 6.3.18: pA(x)=(-1)np(x))
10 M 4/1 Inner Products Sec. 4.1 (again) 4.1.2, 4.1.9, 4.1.10, 4.1.11, 4.1.12
(in 4.1.12: v2 is in W)
Apr 12
W 4/3 Cauchy-Schwarz Sec. 4.2 4.1.4, 4.1.7, 4.1.8, 4.14(a), 4.1.18
F 4/5 Orthonormal Bases Sec. 4.3 4.2.4, 4.2.6, 4.2.8, 4.2.9, 4.2.18
11 M 4/8 Orthogonal Projections Sec. 4.3 (again) 4.3.2(a,b), 4.3.3, 4.3.14, 4.3.22
(in 4.3.14(c): PW(A) = iIm(A))
Apr 19
W 4/10 Least Squares Sec. 4.4 4.3.6, 4.3.8, 4.3.10, 4.3.18
F 4/12 Normed Spaces Sec. 4.5 4.4.1, 4.4.3, 4.4.4, 4.4.5, 4.4.8
12 M 4/15 Isometries Sec. 4.5 (again) 4.4.16, 4.5.1, 4.5.12, 4.5.16, 4.5.17 Apr 26
W 4/17 QR decomposition Sec. 5.1 4.5.4, 4.5.6, 4.5.8, 4.5.10, 4.5.14
F 4/19 Singular Values Sec. 5.2 5.1.4, 5.1.6, 5.1.10, 5.1.14
13 M 4/22 Singular Value Decomposition Sec. 5.3 5.2.2, 5.2.8, 5.2.15, 5.2.20 Not turned in
W 4/24 Adjoint Maps Sec. 5.4 5.3.6, 5.3.8, 5.3.12, 5.3.18
F 4/26 Spectral Theorems None 5.4.2 (b,c), 5.4.6, 5.4.10, 5.4.22