MATH 6118: Topics in Linear Algebra
Spring 1999. University of Colorado at Denver

C A N C E L L E D

Catalog Description:
MATH 6118-3. Topics in Linear Algebra. Infrequent. Topics may include canonical forms, bilinear and quadratic forms, and combinatorial matrix theory. Since the topics will vary each semester, students may register for this course more than once. Prereq: MATH 5718.

HOURS: TR 4-5:15 pm, Central 216 (will likely be moved during the second week of classes)

INSTRUCTOR:
Prof. Andrew Knyazev
Office: CU (Dravo) 644. Phone: 556-8102.
Office hours: by appointment.
WWW: http://www-math.cudenver.edu/~aknyazev

TEXTBOOK:
Matrix Analysis by Roger A. Horn, Charles R. Johnson
Publisher: Cambridge Univ Pr (Pap Txt); ISBN: 0521386322; Reprint edition (July 1990) $35.

ABOUT THE TEXTBOOK: It is one of the references in the APPLIED LINEAR ALGEBRA PRELIMINARY EXAM SYLLABUS. I was one of the translators of this book into Russian in the eighties of the last century.

The following are customer reviews from Amazon.com:

• Not for the uninitiated. Reviewer: yelko from Nagoya, Aichi JAPAN. I bought this book hoping to learn about matrix analysis. I did not. This book is simply a reference manual with plenty of theorems, axioms etc. with little explanation. They give it to you rough and row. NOT A SINGLE SOLVED EXAMPLE, and not even solutions for the exercises given in the book are provided. If you intend to learn about matrix analysis, as I did, let not the 5 stars review mislead you. Don't make the same mistake, this book is not for you.
• An encyclopedic reference for matrix analysis and linear algebra. Reviewer: KARTIK KRISHNAN S. from TROY, NEW YORK USA Horn and Johnson's MATRIX ANALYSIS is simply a masterpiece. You can find each and every result in matrix analysis along with it's proof in this book. Look at their companion volume "Topics in Matrix Analysis" too. Some of these results cannot be found elsewhere.

SUBJECT:
The course will cover several more advanced topics, which are not usually covered by the required 5718 class. Some topics from 5718 will be revisited in a greater depth. There will be no research-level material in this course.

FORMAT:
There will be few traditional lectures and only to cover new material, which does not appear in 5718. Most of the class time will be spend on problem solving, with required student participation. Students will be regularly asked to read and comprehend the corresponding sections before classes in addition to the traditional homework.

This is apparently the first time this class is offered at CU-Denver and the first time this textbook is used. This will also be first time I try such a course format at CU-Denver. Only with student's great help and active participation, this novel course could be successful.

This course might be helpful for preparation for the Applied Linear Algebra Prelim and for the linear algebra part of the comprehensive examination.* To emulate the prelim atmosphere, all written tests will be in-class, closed books. To prepare students for the present format of the comprehensive exam, everybody will be required to participate in solving problems on the board in front of the class and one of the finals will be in the oral format.

CONTENTS:
The class will follow the outline below, touching on each major topic in a depth that will be determined by the pace of the class.

• Ch. 0. Review
• Ch. 1. Eigenvalues, eigenvectors, and similarity
• Ch. 2. Unitary Matrices and Normal Matrices
• Ch. 3. Canonical Forms: 3.0-3.3
• Ch. 4. Hermitian and Symmetric Matrices: 4.0-4.2
• Ch. 5. Norms for Vectors and Matrices: 5.0-5.6
• Ch. 7. Positive Definite Matrices: 7.0-7.3

GRADING:
Written midterm, written final and oral final exams - 20% each. Homework - 20%. In class problem solving - 20%.
(Mathematics is 50 percent knowlegde, 50 percent hard work, and 50 percent imagination.)

Links: LA Books; How to teach linear algebra?.

Other LA courses using the same text at: CU-Boulder (please print these useful notes), URI, NMSU, NCSU, Carleton, IAState.

* There is no explicit or implicit guarantee that every student with a positive grade from this class will pass any preliminary examinations. Individual results may vary.