Course: MATH 115A, Linear Algebra, Lecture 6, Spring 2015
Prerequisite: MATH 33A, Linear algebra and applications.
Course Content: Linear independence, bases, orthogonality, the Gram-Schmidt process, linear transformations, eigenvalues and eigenvectors, and diagonalization of matrices. This course should develop your ability to write rigorous proofs.
Last update: 20 May 2015

Lecture Meeting Time/Location: Monday, Wednesday and Friday, 2PM-250PM, MS 5127
Instructor: Steven Heilman, heilman(@-symbol)
Office Hours: Mondays, 9AM-11AM, Wednesdays 1PM-2PM, MS 7370
TA: Sangjin Lee, sangjinlee(@-symbol)
TA Office Hours: Tuesdays 3PM-4PM, Wednesdays 4PM-5PM, MS 3919
Discussion Session Meeting Time/Location: Tuesdays and Thursdays, 2PM-250PM, MS 5137
Required Textbook: Linear Algebra, Friedberg, Insel and Spence, 4th Ed., Custom Edition for UCLA
Other Textbooks (not required): Linear Algebra: an introductory approach, C. W. Curtis
TA Course Website: here
First Midterm: April 24, 2PM-250PM, KNSY PV 1200B
Second Midterm: May 18, 2PM-250PM, KNSY PV 1200B
Final Exam: June 11, 1130AM-230PM, PAB 1434A
Other Resources: 115A, Tao, Fall 2002: I would highly recommend reading these lecture notes. My own lecture notes below are meant to be a more condensed presentation of similar material. So, if you prefer a more thorough treatment, I recommend these notes (and the book).
An introduction to mathematical arguments, Michael Hutchings, An Introduction to Proofs, How to Write Mathematical Arguments
Exam Procedures: Students must bring their UCLA ID cards to the midterms and to the final exam. Phones must be turned off. Cheating on an exam results in a score of zero on that exam. Exams can be regraded at most 15 days after the date of the exam.
Exam Resources: Here is a page containing old exams for a similar linear algebra course. Occasionally these exams will cover slightly different material than this class, or the material will be in a slightly different order, but generally, the concepts should be close if not identical.
Here are solutions to this second midterm. (Note this practice midterm is much longer than our exam.)
Here are solutions to this practice final. (Skip question 7; also questions 5,6 and 8 are a bit challenging.)

Homework Policy:

Grading Policy:

Tentative Schedule: (This schedule may change slightly during the course.)

Week Monday Tuesday Wednesday Thursday Friday
1Mar 30: 1.2, Vector spacesApr 1: 1.3, Subspaces Apr 2: No homework dueApr 3: 1.4, 1.5, Linear systems, Linear independence
2Apr 6: 1.5, 1.6, Linear independence, basesApr 8: 1.6, Dimension Apr 9: Homework 1 dueApr 10: 2.1, Linear transformations
3Apr 13: 2.1, Linear transformations Apr 14: 1.6, Lagrange interpolation Apr 15: 2.1, 2.2, Null spaces, range, coordinate bases Apr 16: Homework 2 dueApr 17: 2.2, Matrix representation
4Apr 20: 2.3, Matrix Multiplication Apr 22: 2.4, Invertibility Apr 23: Homework 3 dueApr 24: Midterm #1
5Apr 27: 2.4, IsomorphismApr 29: 2.4, 2.5, Change of coordinates Apr 30: Homework 4 dueMay 1: 3.1-4.3, Row operations
6 May 4: 3.1-4.3, Rank of matricesMay 6: 4.4, Review of determinants May 7: Homework 5 dueMay 8: 5.1, Diagonal matrices
7May 11: 5.1, Eigenvalues and eigenvectors May 13: 5.2, DiagonalizationMay 14: Homework 6 due May 15: 5.2, Characteristic polynomials
8May 18: Midterm #2 May 20: 6.1, Inner productsMay 21: No homework due. May 22: 6.1, 6.2, Norms, orthogonal bases
9May 25: No class May 27: 6.2, Gram-Schmidt orthogonalization, complementsMay 28: Homework 7 due May 29: 6.3, Adjoints
10Jun 1: 6.4, Normal operators Jun 3: 6.4, Self-adjoint operators Jun 4: Homework 8 dueJun 5: Review of course

Advice on succeeding in a math class:

Homework Exam Solutions Supplementary Notes