Linear Algebra and Lab II

Course Information

Textbook: Contemporary Linear Algebra by Howard Anton and Robert C. Busby

Classes: Mon 14~16, Wed. 11~13

Labs: Time and place will be announced when necessary.

Grades: 2 Midterms (200 points), Final Exam (100 points), Homework, Projects and Quizzes (100 points)

Instructor's Office Hours: Mon 16~17; Wed 14~15 (Room 417) or by appointment

Teaching Assistants: Jang, Deokgyu dkjang@kangwon.ac.kr (Room 419 Office hour: Mon 9~11; Thr 14~16 or by appointment)

Park, Joosung js-park@kangwon.ac.kr (Room 419 Office hour: Mon 9~11; Thr 14~16 or by appointment)

Announcement

• 12/23 (2~4pm) Monday, Final exam covers normal matrix in Chapter 8, Chapter 9 and Jordan form
• Problems for Jordan Form. Click here for solutions.
• Supplementary lecture schedule: Dec. 9; Dec.16; Dec. 19 (Time 11am~1pm)
• 11/27 Wednesday, Midterm 2 covers Chapter 8
• Extended office hours for Midterm 2: 11/20 Wed. (Kang 15~16) 11/21 Thr. (Jang 9~11 and 13~14; Park 9~11) 11/22 Fri. (Park 12~14; Jang 9-12) 11/25 Mon.(Jang 9~11) 11/26 Tue. (Jang 13~14 and 16~18)
• 10/21 Monday, Midterm 1 covers Chapter 7
• Extended office hours for Midterm 1: 10/14 Mon.(Jang 9~11) 10/15 Tue. (Jang 13~14 and 16~18) 10/16 Wed. (Kang 16~17) 10/17 Thr. (Kang 16~17; Jang 9~11 and 13~14; Park 9~11) 10/18 Fri. (Park 12~14; Jang 9-12)

Topics covered in class

• 9/2 Review 1 - Linear Algebra and Lab I
• 9/4 Review 2 - Linear Algebra and Lab I
• 9/9 Section 7.3 Fundamental spaces
• 9/11 Section 7.4 Dimension theorem of matrices, dimension theorem of subspaces, rank 1 matrices, constructing a basis for n-space from a linearly independent subset
• 9/16 Section 7.5 and 7.6 Rank theorem, pivot theorem, the consistency theorem, full column (row) rank, over and under determined case of linear systems, algorithms for finding bases for fundamental spaces
• 9/23 Section 7.5 and 7.6 CR factorization of a matrix, matrices of the form A(A^T) and (A^T)A
• 9/30 Section 7.7 Orthogonal projection on a subspace and its perp
• 10/2 Section 7.9 Orthonormal bases and Gram-Schmidt Process
• 10/7 Section 7.10 QR-decomposition of a matrix with full column rank
• 10/14 Section 7.8 Best approximation, least squares solution, least square error, least squares line (or curve) of best fit
• 10/16 Section 7.11 Coordinates with respect to a basis, change of basis, transition matrix
• 10/23 Section 8.1 Matrix representation of linear transformations
• 10/28 Section 8.2 Similar matrices, similarity invariance
• 10/30 Section 8.2 Diagonalizable matrix
• 11/4 Section 8.2 and 8.3 Algebraic and geometric multiplicities of eigenvalues of a matrix and its diagonalization; orthogonal diagonalization
• 11/6 Section 8.3 orthogonal diagonalizability, spectral decomposition, powers of a matrix
• 11/11 Section 8.3 function of a matrix, Cayley-Hamilton theorem, power series of a matrix
• 11/13 Section 8.4 quadratic forms, orthogonal change of variables to diagonalize quadratic forms
• 11/18 Section 8.6 singular value decomposition; reduced singular value expansion of a matrix; pseudoinverse
• 11/20 Section 8.8 complex n-space, complex Euclidean inner product
• 11/25 Section 8.9 Hermitian and unitary matrix, unitarily diagonalizable matrix
• 12/2 Section 8.8 and 9.1 Normal matrix, general vector space axioms
• 12/4 Section 9.1 Finite and inifinite-dimensional vector spaces, Wronski's test for linear independence of functions, Lagrange interpolatin gpolynomials
• 12/9 Section 9.2 inner product axioms, inner product space, positive definite quadratic forms
• 12/16 Section 9.2 and 9.3 Complex inner product space, general linear transformation
• 12/19 Section 9.3 Every real n-dimensional vector space is isomorphic to Rn ; Jordan form

Homework Assignments

• Set 1 (due 9/16) p.349 #2,4,8,10,12,16,18,20,22,24,26,28,30,32 p.351 #D3,D6,P4; p.357 #4,8,10,12,14(b),20,22 p.359 #D3,D6,D8,P2
• Set 2 (due 9/23) p.368 #2,4,6,8,10(b,d),14,18 p.369 #P4,P5; p.377 #2,4,8,12,14, p.378 #D1
• Set 3 (due 9/30) p.368 #12(b,d),16 p.369 #D2,D4,P3; p.378 #16,D3,D4
• Set 4 (due 10/7) p.391 #2,4,8,12,14,18,20,22,24,26; p.414 #2(d),4(b),6(a),8(b),10,12,14,18,28,30,32,34,36,38
• Set 5 (due 10/14) p.416 #D1~D6; p.426 #2,4,6,25
• Set 6 (due 10/21) p.404 #2,4,6,8,10,12,14; p.438 #4,6,8,12,14,16,18,24
• Set 7 (due 10/28) p.453 #6,8,10,12,14,16,20,22,24,26
• Set 8 (due 11/4) p. 466 #2,4,6,8,12,16,20,22,26,30,31,32
• Set 9 (due 11/11) p.479 #4,6,8,10,12,14,16,18,20,22
• Set 10 (due 11/18) p.479 #26,28,30; p.480 #D2,P3; p.492 #2,4,6,8,10,12,14,16,32
• Set 11 (due 11/25) p.516 #2,4,8,10,12,16,18,19; p.523 #8,12; p.532 #2,4,6,8,10,12,14,18,22
• Suggested problems p.539 even numbered problems among #1~24
• Set 12 (due 12/9) p.539 #26,30,32; p.566 #4,6,8,12,14,16,20,22,24,26
• Set 13 (due 12/16) p.580 #2,4,6,10,12,14,16,18(a,b),26
• Suggested problems p.580 and p.592 odd numbered problems

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