Linear Algebra II
Math 262 - Spring 2019
Announcements
The semester is over.
About the course
Linear algebra is a central subject of mathematics which has applications not only in mathematics itself but also in statistics, economics, physics and engineering (just to name a few).
By the end of the course, the students should have a detailed understanding of how to use the eigenvalue and eigenvector concept, the diagonalization process, the canonical forms of linear operators, the structure of inner product spaces.
Schedule of Lectures and Office Hours
Lectures: Tuesday and Thursday between 13:40-15:30 in M13.
Attendance will not be taken during the lectures. However, I strongly suggest that you shall attend the lectures regularly.
Office hours: Tuesday between 10:40-12:30 in M141.
If these office hours are not suitable for you, then you shall send me an email (komer@metu.edu.tr) to fix an appointment.
Suggested Problems
The following is a list of suggested problems from our textbooks. These questions are from the first textbook, namely Friedberg, Insel, Spence - Linear Algebra, 4th edition.
Section 5.1: 1, 2, 3, 4, 7, 8, 9, 12, 15, 17, 20.
Section 5.2: 1, 2, 3, 7, 8, 9, 11, 12, 20, 21, 22.
Section 5.4: 1, 2, 5, 6, 8, 9, 11, 13, 16, 17, 18, 19, 21, 33, 36, 38.
Section 6.1: 1, 2, 4, 5, 8, 9, 10, 11, 17, 18, 19, 20, 24, 25, 27h.
Section 6.2: 1, 2, 3, 5, 6, 7, 9, 11, 13, 14, 15, 18, 19, 21, 22, 23.
Section 6.3: 1, 2, 3, 6, 7, 8, 9, 10, 11, 12, 13, 14.
Section 6.4: 1, 2, 4, 6, 7, 8, 9, 10, 11, 12, 15, 17, 18, 19, 20.
Section 6.5: 1, 2, 4, 5, 6, 7, 9, 11, 12, 13, 15, 16, 17, 18, 21, 27, 28.
Section 6.6: 1, 2, 4, 5, 6.
Section 6.8: 1, 3, 4, 5, 6, 7.
Section 7.1: 1, 2, 3, 4, 5, 6, 7.
Section 7.2: 1, 2, 3, 4, 5, 6.
Section 7.3: 1, 2, 3, 4, 5, 6.
Section 7.4: 1, 2, 3, 4, 5.
Grading
Your final letter grade will be determined by two midterms and the final exam. The exam dates are as below.
Midterm 1 and Solutions - March 19 (%30)
Midterm 2 and Solutions - April 17 (%30)
Final and Solutions - May 24 (%40)
Textbooks
I will use the following books when I prepare my notes and assign exercise problems:
The first textbook is Friedberg, Insel, Spence - Linear Algebra, 4th edition. It is available in the reserve part of the library with code QA184.F75.
The second textbook is Cemal Koç - Topics in Linear Algebra which is the classical linear algebra book of our department for the second semester.
Tentative Course Outline
You can find the tentative course outline below. For each week, we will attempt to cover the content of the indicated pages of Friedberg, Insel, Spence - Linear Algebra (4th edition).
(Feb 12, Oct 14) Eigenvalues and Eigenvectors, 245-260.
(Feb 19, Feb 21) Diagonalizability 261-272.
(Feb 26, Feb 28) Direct Sums 274-283. Invariant Subspaces and the Cayley-Hamilton Theorem, 313-327.
(Mar 5, Mar 7) Inner Products and Norms, 329-340.
(Mar 12, Mar 14) The Gram-Schmidt Orthogonalization Process, 341-356.
(Mar 19, Mar 21) The Adjoint of a Linear Operator, 357-368.
(Mar 26, Mar 28) Normal and Self-Adjoint Operators, 369-378.
(Apr 2 - Apr 4) Unitary and Orthogonal Operators and Their Matrices, 379-397.
(Apr 9 - Apr 11) Orthogonal Projections and the Spectral Theorem, 398-404.
(Apr 16 - Apr 18) Bilinear and Quadratic Forms, 422-450.
(Apr 23, Apr 25) The Jordan Canonical Form I, 482-496.
(Apr 30, May 2) The Jordan Canonical Form II, 497-515.
(May 7, May 9) The Minimal Polynomial, 516-523.
(May 14, May 16) The Rational Canonical Form, 524-547.
Make-up and NA policy:
Only one make-up examination will be offered. The excuse for not attending an examination must be proved with documents. The make-up examination will take place shortly after the final exam. If you have missed both midterms, your letter grade would be NA. If you receive NA, then you can not take the final exam and the makeup.
SageMath
The software SageMath is very simple to learn and
extremely strong to do computations with.