Course: MATH 115A, Linear Algebra, Lecture 6, Fall 2014
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: 11 December 2014

Lecture Meeting Time/Location: Monday, Wednesday and Friday, 1PM-150PM, MS5147
Instructor: Steven Heilman, heilman(@-symbol)
Office Hours: Mondays, 930AM-1130AM, Fridays, 1030AM-1130AM, MS 7370
TA: Geunho Gim, ggim(@-symbol)
TA Office Hours: Thursdays, 9AM-11AM, MS 2344
Discussion Session Meeting Time/Location: Tuesday and Thursday, 1PM-150PM, MS5147
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: October 31, 1PM-150PM, FRANZ 2258A
Second Midterm: November 24, 1PM-150PM, PUBLIC AFFAIRS 2250
Final Exam: December 15, 8AM-11AM, BOELTER 5440
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
0Sep 29 Oct 2: No homework dueOct 3: 1.2, Vector spaces
1Oct 6: 1.3, Subspaces Oct 8: 1.4, 1.5, Linear systems, Linear independenceOct 9: No homework due Oct 10: 1.5, 1.6, Linear independence, bases
2Oct 13: 1.6, Dimension Oct 15: 1.6, Lagrange interpolationOct 16: Homework 1 due Oct 17: 2.1, Linear transformations
3Oct 20: 2.1, Linear transformations Oct 22: 2.1, 2.2, Null spaces, range, coordinate bases Oct 23: Homework 2 due Oct 24: 2.2, Matrix representation
4Oct 27: 2.3, Matrix Multiplication Oct 29: 2.4, InvertibilityOct 30: Homework 3 dueOct 31: Midterm #1
5Nov 3: 2.4, Isomorphism Nov 5: 2.4, 2.5, Change of coordinatesNov 6: Homework 4 due Nov 7: 2.5, Change of coordinates
6Nov 10: 3.1-4.3, Review of matrices Nov 12: 4.4, Review of determinantsNov 13: Homework 5 dueNov 14: 5.1, Diagonal matrices
7Nov 17: 5.1, Eigenvalues and eigenvectors Nov 19: 5.2, DiagonalizationNov 20: Homework 6 dueNov 21: 5.2, Characteristic polynomials
8Nov 24: Midterm #2 Nov 26: 6.1, Inner productsNov 27: No classNov 28: No class
9Dec 1: 6.1, 6.2, Norms, orthogonal bases Dec 3: 6.2, Gram-Schmidt orthogonalization, complementsDec 4: Homework 7 dueDec 5: 6.3, Adjoints
10Dec 8: 6.4, Normal operators Dec 10: 6.4, Self-adjoint operatorsDec 11: Homework 8 dueDec 12: Catch up, review

Advice on succeeding in a math class:

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