MATH2040A/B - Linear Algebra II - 2014/15

Announcement

• HW posted. No need to hand in your HW.
• Review on simple questions: Jan 29 Thu 7:30pm-9pm LSB LT4
• Review on Midterm I :Feb 5 Thu 7:30pm-9pm LSB LT4
• Midterm up to Lecture 8 Sect 1, Textbook Sect 1.3 to 2.4
• Office hr: Monday 2:30 to 4pm, Tue 4:15 to 5:45
• Tutorial ex 6 has been posted. If you decide not to attend tutorial, you can hand it in on Mar 2 Mon before 5pm. Instruction is given in the file. [Download file]
• Review: Mar 12 7:30-9:00pm LSB LT2
• Five set of questions for midterm II are posted. A review note will be posted.
• I reserve rooms MMW707 Mar 16 Mon, 3:30-5:00 and LHC G04 Mar 17 Tue 4:00-6:00. You can study in the classroom and I will be there in case your have qusetions. .
• You can also get help from mathgym Mathgym website
• A study guideline has been posted [Download file]
• Tutorial ex 12 has been posted. Students from Tue TA session can hand it in on Thu. [Download file]
• Final review [Download file]
• Final review (printable version, same as the powerpoint version above) [Download file]
• Final computational exercises [Download file]

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General Information

Lecturer

• Charles Li
  • Office: LSB218
  • Tel: 3943-7974
  • Email:

Teaching Assistant

• Cho Ki Kit Edward
  • Office: Room 233, LSB
  • Tel: 3943 7956
  • Email:
• Zuo Cheng
  • Office: Room 222C, LSB
  • Tel: 3943 8570
  • Email:
• Gu Dalin
  • Email:

Time and Venue

• Lecture: 2040A: Tu 2:30-4:15 YCL G04, Th 12:30-1:15 LSB LT2, 2040B 12:30-1:15 LSB LT5, 2:30-4:15 LSB LT5

Course Description

This is a continuation of MATH1030. Topics include: linear mapping and its matrix representation, eigenvalues and eigenvectors, inner product spaces, Gram-Schmidt process, Jordan canonical forms.

Textbooks

• Friedberg, Insel, Spence, Linear Algebra, 4th edition, Prentice Hall

Lecture Notes

• Lecture 0: class info
• Lecture 1: Vector space
• Lecture 2: Subspace
• Lecture 3: Linear combination
• Lecture 4: Linear dependence
• Lecture 5: Basis
• Lecture 6: Linear transformatoin
• Lecture 7: Matrices and Linear transformations
• Lecture 8: Standard representation and change of coordinates
• Summary about notation [T]
• Lecture 9: Diagonalization
• Lecture 10: Diagonalization II
• Lecture 11: Diagonalization III
• Lecture 12: Direct Sum
• Lecture 13: Invariant subspace, T-cyclic subspace, Cayley-Hamition theorem
• Lecture 13: computational example on T-cyclic subspace
• Lecture 14: Inner product space
• Lecture 15: Gram-Schmidt orthogonalization
• Lecture 16: Adjoint
• Lecture 17: Normal and Self-adjoint operators
• Lecture 18: Unitary and orthogonal operators
• Lecture 19: projection, spectrum theorem

Tutorial Notes

• Tutorial ex 1
• Tutorial ex 1 answer
• Tutorial ex 2
• Tutorial ex 2 answer
• Tutorial ex 3
• Tutorial ex 3 answer
• Tutorial ex 4
• Tutorial ex 4 answer
• Tutorial ex 5
• Tutorial ex 5 answer
• Tutorial ex 6
• Tutorial ex 6 answer ( Q5c has a typo, fixed)
• Tutorial ex 7
• Tutorial ex 7 answer
• Tutorial ex 8
• Tutorial ex 8 answer
• Tutorial ex 9
• Tutorial ex 9 answer
• Tutorial ex 10
• Tutorial ex 10 answer
• Tutorial ex 11
• Tutorial ex 11 answer
• Tutorial ex 12
• Tutorial ex 12 answer
• Tutorial ex 13
• Tutorial ex 13 answer
• Formula table for ex 11

Assignments

• HW1: Sect 1.2 Q13, 17, 19, 20, 21
• HW2: Sect 1.3 Q14, Q19, Q22, Q23, Sect 1.4 Q10, Q13, Q15, Q16
• HW3: Sect 1.5 Q15, 16, 19, Sect 1.6 Q12, 17, 21, 23
• HW4: Sect 1.6 Q29, 31, Sect 2.1 Q14, 17, 18, 20, 26
• HW5: Sect 2.2 Q11, Q13, Q16, Sect 2.3 Q11, Q12, Q16 Sect 2.4 Q16, Q20, Q21
• HW6: Sect 2.5 Q8, Q13, Sect 5.1 Q8a, b, Q9, Q11, Q15
• HW7: Sect 5.1
• HW8: Sect 5.2
• HW9: Sect 5.4
• Sect 6.1-6.6

Quizzes and Exams

• Review on Jan 29: simple exercises
• 2014 Midterm I
• 2014 Midterm I soluton
• Midterm I review
• Midterm I more sample questions
• 2015 Midterm 1
• 2015 Midterm I solution
• Midterm II Exercise 1 (with solution)
• Midterm II Exercise 2 (with solution)
• Midterm II Sample 1
• Midterm II Sample 1 Answer
• Midterm II Sample 2
• Midterm II Sample 2 Answer
• Midterm II Sampe 3 (important typo: for Q5 (b), add "U is diagonalizable")
• Midterm II Sampe 3 Answer
• Midterm II Study Guidline
• Midterm II review
• Midterm II review printable version (same as the above version)
• 2015 Midterm II
• 2015 Midterm II Answer
• Fianl review
• Final review printable version (same as the above version)
• Final computational exercises
• Table for operators

Solutions

• HW1 Solution (reference only)
• HW2 Solution (reference only)
• HW3 Solution (reference only)
• HW4 Solution (reference only)
• HW5 Solution (reference only)
• HW6 Solution (reference only)
• Solution for the textbook Sect 1.3 (reference only, last updated: Jan 31)
• solution for the textbook Sect 1.4 (reference only, last updated: Jan 31)
• Solution for the textbook Sect 1.5 (reference only, last updated: Jan 31)
• Solution for the textbook Sect 1.6 (reference only, last updated: Jan 31)
• Solution for the textbook Sect 2.1 (reference only, last updated: Jan 31)
• Solution for the textbook Sect 2.2 (reference only, last updated: Jan 31)
• Solution for the textbook Sect 2.3 (reference only, last updated: Jan 31)
• Solution for the textbook Sect 2.4 (reference only, last updated: Feb 7)
• Textbook Sect 2.5, 5.1, 5.2, 5.4 Questions
• Solution for the textbook Sect 2.5 (reference only, last updated: Feb 25)
• Solution for the textbook Sect 5.1 (reference only, last updated: Feb 25)
• Solution for the textbook Sect 5.2 (reference only, last updated: Feb 25)
• Solution for the textbook Sect 5.4 (reference only, last updated:Mar 5)
• Text Sect 6.1 - 6.6 Exerciese (printout given during class)
• Solution for the textbook Sect 6.1 (reference only, last updated: April 1)
• Solution for the textbook Sect 6.2 (reference only, last updated: April 1)
• Solution for the textbook Sect 6.3 (reference only, last updated: April 1)
• Solution for the textbook Sect 6.4 (reference only, last updated: April 1)
• Solution for the textbook Sect 6.5 (reference only, last updated: April 1)
• Solution for the textbook Sect 6.6 (reference only, last updated: April 1)

Assessment Scheme

Tutorial: You have to attend at least 8 tutorials session. Each tutorial accounts for 1pt.		8%
Midterm 1: Feb 10 Tue 7:30 - 9:30 pm LSB LT1		18.5%
Midterm 2: Mar 17 Tue 7:30 - 9:30 pm LSB LT1		18.5%
Final		55%

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Last updated: April 16, 2015 14:11:03