Soon-Yi Kang's Homepage

Courses

Linear Algebra and Lab II

Course Information

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

Reference: Linear Algebra by Stephen Friedberg, Arnold Insel and Lawrence Spence

Classes: Mon, Tr. 11~13

Labs: Time and place will be announced when necessary.

Grades: 2 Midterms (200 points), Final Exam (150 points), Homework, Projects and Quizzes (150 points)

Instructor's Office Hours: W 1~2 pm (Room 417) or by appointment

Teaching Assistants: Jang, Deokgyu (장덕규) dkjang@kangwon.ac.kr (Room 419 Office hour: Tue 4~5pm or by appointment)

Park, Joosung (박주성) js-park@kangwon.ac.kr (Room 419 Office hour: Fri 11~12pm or by appointment)

Announcement

12월 13일 목요일 (11am~1pm): Final Exam covers Jordan Canonical Forms and Inner Product Spaces
12월 5일 2시, 12월 6일 11시 강의보충
중간고사2 해답
11월 5일 월요일: Midterm 2 covers matrix representations of vectors and linear transformations and diagonalization, including Cayley-Hamilton Theorem
대동제로 인하여 9월27일 수업은 휴강입니다.
중간고사1 해답
Midterm Review Sheet (질문형식으로 주어진 기본적인 개념)
9월 24일 월요일: Midterm 1 covers general vector spaces and linear transformations

Topics covered in class

12/6 Orthogonal projection and spectral decomposition
12/5 Unitary and orthogonal operators; conic sections
12/3 Schur Theorem; Existence of orthonomal basis consisting of eigenvectors of a normal operator on a finite-dimensional complex inner product space; Existence of orthonomal basis consisting of eigenvectors of a Hermitian operator on a finite-dimensional real inner product space
11/29 The adjoint of a linear operator; normal and Hermitian operators
11/26 Gram-Schmidt orthogonalization and orthogonal complement (see Sections 7.7 and 7.9 for n-spaces)
11/22 Inner products and norms
11/19 Dot diagram for a linear transformation or matrix associated with a basis
11/12 Linear independence of a cycle of a generalized eigenvector and disjoint union of cycles of generalized eigenvectors, finding Jordan form
11/8 Introduction to Jordan canonical form, Jordan block, Jordan canonical basis, generalized eigenvectors, generalized eigenspaces
11/1 Cayley-Hamilton Theorem; minimal polynomial
10/29 Sufficient and necessary conditions for diagonalizability; Algorithm for diagonalization
10/25 Characteristic polynomials of an operator; a sufficient condition for an operator to be diagonalizable; Eigenspace
10/22 Diagonalization problem, Eigenvalues and eigenvectors of operators and matrices (refer Section 8.2 for n-spaces)
10/18 Effect of changing bases on matrices of linear transformations (refer Section 8.1 for n-spaces); Similar matrices represent a same linear operator; Diagonalizable operator and matrices (refer Section 8.2 for n-spaces)
10/15 Coordinates with respect to a basis (refer Section 7.11 for n-spaces); Change of bases (refer Section 8.1 for n-spaces)
10/11 Matrix representations of linear transformations (refer Section 8.1 for n-spaces)
10/8 The set of linear transformations from a vector space V over F to a vector space W over F forms a vector space over F; This space is isomorphic to the space of m by n matrices over F where dim(V)=n and dim(W)=m
9/20 Linear transformation is completely determined by its action on a basis, Isomorphism, the space of linear transformations
9/17 Kernel, range, one-one, onto, nullity, rank, dimension theorem
9/13 Direct sum of subspaces; Section 9.3 General linear transformation
9/10 Subspaces of a vector space and their dimensions, intersection spaces, sum spaces
9/6 Bases and Dimenstions for general vector spaces continued, including Lagrange interpolation formula
9/3 Bases and Dimenstions for general vector spaces
8/30 Section 9.1 Spanning set, linearly independent set, linearly dependent set, basis of a vector space, dimension theorem for a finite-dimensional vector space
8/27 Section 9.1 Vector space Axioms, definitions of a general vector space, subspace and their examples

Homework Assignments

Set 1 (Due 9/3) p.566 #2,4,5,6 (See Example 2 on p.556 for the definition of Roo.), 7,9,10,12,13,20,22,27,32
Set 2 (Due 9/10 Click here for Problems and p.568 #24 Solutions of HW
Set 3 (Due 9/17) Click here for Problems and p.592 #2,4,9 Solutions of HW
p.593 Odd numbered problems (Suggested problems들로 이번 숙제는 제출하지 않습니다.)
Extra HW (Due 10/11) Show the ontoness of the linear map defined in class from the space of linear transformations into the space of matrices
Set 4 (Due 10/15) Click here for Problems and p.453 #2,6,16 (1번은 보너스 문제) Solutions of HW
Set 5 (Due 10/22) p.438 #4,6,16,20 (see Example 7 for row reduction),26,27, p.453 #4,8,14,18,20 (we used [T]bb' for the notation [T]b',b ),26,28, p.466 #2,4
Set 6 (Due 10/29) Click here for Problems p.466 #6,8,12,14,18,25,27,30 Solutions of HW
Click here for suggested Problems p.479 #19,21,23,31 Solutions for suggested problems
(Due 11/12) Prove the disjointness of generalized eigenspaces corresponding to different eigenvalues
Set 7 (Due 11/19) Click here for Problems Solutions of HW
Set 8 (Due 11/26) Click here for Problems Solutions of HW
Set 9 (Due 12/3) Click here for Problems p.414 #2(c),4(b),6(a),8(b),10,12,28,30,36,38 Solutions of HW
Click here for suggested Problems