Math 113: Linear algebra and matrix theory

Akshay Venkatesh, MWF 10am in room 380-380X.

The final exam has been graded, and grades posted. The exam was out of 80 points; however, anything above 60 was considered excellent. The median score was in the 40s.
Happy holidays!
The practice final is here.
A correction to the second part of Problem 8: The assumption should be that there exists a k-dimensional subspace Q so that ||T v|| >= ||v|| for every v in Q. The question as stated was wrong! Can you find a counterexample?
A second correction (thanks to Julie Ralph): Question 3, second part: The definition of the subspace should be image of T contained in I, not equal to I.

Here are some solutions: solutions.

From the course bulletin: Algebraic properties of matrices and their interpretation in geometric terms. the relationship between the algebraic and geometric points of view and matters fundamental to the study and solution of linear equations. Topics: linear equations, vector spaces, linear dependence, bases and coordinate systems; linear transformations and matrices; similarity; eigenvectors and eigenvalues; diagonalization.

Translation: this is a ``theoretical'' introduction to linear algebra, emphasizing abstract structures (vector spaces, linear transformations) as opposed to vectors and matrices. It's also intended to give you an introduction to writing mathematical proofs.

Text: We will use the text Linear Algebra done right by Sheldon D. Axler. As a supplement, we will often use the notes A (terse) introduction to linear algebra, by Prof. Katznelson. A summary of what is in each lecture will be posted below, together with a reference to the text.

Office hours, graders, CA: My office hours will be Monday 2--4pm. The CA is Ha Pham; office hours Tuesday 6-7, Thursday 5--7pm in room 381-K (NOTE CHANGE).

Grading: (Weekly) homework 25%, midterm 25%, final 50%.
Homework will be due by Friday 5pm outside my office. The first homework will be due on Friday, October 3.

Note: I will discount the lowest score when computing the homework grade. Thus, if you miss one homework, it will not affect your grade.

Approximate syllabus. I hope to cover most of the text. For the first three weeks, I expect we will cover roughly one chapter of Axler's book each week, beginning with Chapter 1. However, we will skip around a little at first, and more as the course continues; we will make more use of determinants than Axler. Updated mid-October: In the fourth week, we covered dual spaces; now, in the fifth week, we are covering determinants. In future weeks we will return to proceeding through Axler. updated start of December We covered Axler up to, and including, Chapter 8. We did not cover Chapter 9, and this will not be on the final; as for Chapter 10, we have covered determinant but not trace.

For an accurate indication of what we are doing, see lecture summaries below, which will include text references.

Information about the midterm, held on October 17, is here.
Summaries are now here.
Notes: Ilya Sherman has kindly allowed his class notes to be posted; notes through October 25 are here; continued 10-28, 10-30, 10-31, 11-03, 11-05, 11-07, 11-10, 11-12, 11-14, 11-17, 11-19.
Problem sets: See HERE!!
Akshay Venkatesh
Department of Mathematics Rm. 383-E
Stanford University
Stanford, CA
email: akshay at stanford math