# Matrix Analysis

## COURSE MATERIALS

Schedule and Homework (Updated Daily)
Syllabus [pdf]

## PROJECT

The \$25,000,000,000 Eigenvector: The Linear Algebra Behind Google [pdf]
by Kurt Bryan and Tanya Leise, SIAM review, Vol. 48, Num. 3, Sept. 2006, pp. 567-581.

Clarification of some of the Exercises in the paper

Exercise 14: Be aware that you may encounter numerical errors when performing convergence experiments due to the finite representation of real numbers on a computer.

Exercise 15: The last three sentences are poorly worded.
Replace the third last sentence with: Show that the sum of the components in each v_j must equal 0i, and hence that a=1.
Replace the last sentence with: Finally determine M^k x_0 and evaluate the limit [given at the end of ex 15].
In addition, use the limit you computed to find an upper bound on the the error || M^k x_0 -q ||_1 in the power method. Hint: See the proof of the Ratio Test in Calculus II.

Exercise 16: You may compute the eigenvalues and eigenvectors analyticaly or using the symbolic computation features of Matlab's Symbolic Math Toolbox

Exercise 17: There are several possible answers to this problem. I think the best answer involves the rate of convergence of the power method and the result on the top of page 580 of the paper that |lambda_2| is less than or equal to 1-m. For more information on the power method and its rate of convergence see Examples 7.3.5 and 7.3.7 of Meyer's book as well as Wikipedia.

## PAST EXAMS

Note that in Fall 2005 and 2006 I covered the material in a different order than it will be covered this semester. Therefore the content covered on the midterm exam one (two) this semester will not be the same as for exam one (two) of the past exams.

## Exams from Matrix Analysis in Fall 2005

Exam One [pdf]
Exam One Solutions [pdf]
Exam Two [pdf]
Exam Two Solutions [pdf]
Final [pdf]

## Exams from Matrix Analysis in Fall 2006

Exam 1 [pdf]
Exam 1 Solutions [pdf]
Exam 2 [pdf]
Exam 2 Solutions [pdf]

## Information Re Exam One

Exam I will cover 1.2, 1.3, 2.1, 2.2, 2.3, 2.4, 2.5, 3.1-3.7, 4.1-4.4.

Exam One [pdf]
Solutions to Exam One [pdf]

## Information Re Exam Two

Exam II will cover 4.3-4.8, 5.3-5.6, 5.9-5.11.
Solutions to Exam Two [pdf]

## Final Exam

Final Exam [pdf]

Solutions to Final Exam [tif]