Math 2275 continues from where Math 2255 left off. In this course we learn about real eigenvalues and eigenvectors, orthogonality and least squares, and symmetric matrices and quadratic forms.

Last Updated: April 24, 2006

• April 24, 2006 I have finished grading the exams. Your marks are below: Math 2275 Unoffical Final Marks
• April 6, 2006 The last assignment has been graded and can now be picked up. You can also check out your grade (minus the final): Math 2275 Pre-Exam Marks
• March 29, 2006 Today was our last class for the semester, so we did some review. I also gave out your last homework assignment. Please bring your assignment to my office anytime before Wed., April 5 at noon.
• March 27, 2006 Today we finished Section 7.4. I did another example on singular value decomposition. Make sure you understand this method -- there will be a question about it on the exam.
• March 24, 2006 We continued Section 7.4 on the singular value decomposition. You will need to know how to carry out this decomposition. Also, the exam review sheet was handed out.
• March 23, 2006 I added the review sheet for the final.
• March 22, 2006 Today we started looking at Section 7.4 on Singular Value Decomposition. There is a lot of important material in this section, so please read this section carefully.
• March 20, 2006 We finished Section 7.3. I also handed back the second midterm.
• March 17, 2006 We began Section 7.3 on constrained optimization.
• March 15, 2006 Midterm II was today.
• March 13, 2006 We finished Section 7.2 on quadratic forms. You should the terms positive definite, negative definite, and indefinite. Also know the prinicpal axes theorem. HWA 6 is available outside my office.
• March 10, 2006 We started Section 7.2 on quadratic forms.
• March 8, 2006 We finished Section 7.1 on diagonalizing a symmetric matrix.
• March 7, 2006 The last challenge assignment was added to the web.
• March 6, 2006 We started Section 7.1 on the diagonalization of symmetric matrix. Know what it means for a amtrix to be orthogonally diagonalizable. I also added HWA 7 to the web.
• March 3, 2006 START STUDYING! The next midterm is March 15. The review sheet is now available on the web.
• March 3, 2006 We looked at Section 6.8 on applications of inner product spaces. In particular, we looked at Fourier series, which allows us to approximate continuous functions by linear combinations of sines and cosines. See pages 440-442 of the text.
• March 1, 2006 Today we finished looking at Section 6.7 on inner product spaces. We showed how to an inner product to find projections and to find orthogonal bases. We also looked at the vector space formed by all the continuous functions on the interval [a,b]. We showed how one could but an inner product on this space using calculus. HWA 4 was handed back, and HWA 5 was due in class today.
• Feb. 27, 2006 Welcome back from break! Today we introduced the notion of an inner product for any vector space. Understand the examples described in class. Know how to use this inner product to define a notion of length. Also know the Cauchy-Schwarz and Triangle inequalities.
• Feb. 17, 2006 We looked at Section 6.6 -- we discussed how to use least squares solution to find linear or quadratic equations to model a collection of data points. Have a good break!
• Feb. 15, 2006 We finished Section 6.5 by discussing two other ways in which a least squares solution can be solved. HWA 4 and Challenge Assignment 2 were due today.
• Feb. 13, 2006 We looked at Section 6.5 on least squares solutions. Be able to do problem like those discussed in class. Also know what is meant by the normal equations.
• Feb. 10, 2006 We discussed Section 6.4 in class. After today's class, you should know how to use the Gram-Schmidt method to find an orthogonal basis for a subspace. Also, you should know how to use the method to find orthonormal bases and to find the QR-factorization of a matrix. I handed back the midterm as well.
• Feb. 8, 2006 Today was the first midterm. A new HWA was also given out. I also added a new challenge assignment.
• Feb. 6, 2006 We continued with Section 6.3 by discussing the properties of orthogonal projections. You should know the how to use the best approximation theorem, and how to use an orthonormal basis to find the projection of a vector. HWA 3 was handed back.
• Feb. 3, 2006 Today we finished Section 6.2, and started Section 6.3. Know what an othornormal set is, and also how to decompose a vector into two verctors as done in Theorem 8.
• Feb. 1, 2006 We finished Section 6.1. Know what an orthogonal set is, and what an orthogonal basis is. We then started discussing Section 6.2 on orthogonal projections. HWA 3 and Challenge assignment 1 were due today. HWA 2 was handed back.
• Jan. 30, 2006 We started a our discussion of Chapter 6. We looked at Section 6.1 -- you should know the terms norm, inner product, and orthogonal. Also know what we mean by the "perp" of a subspace. I also handed out the review sheet for the first midterm. You can also download a copy from this website (in the column to the left).
• Jan. 27, 2006 We discussed the material of Section 5.8 which gave an iterative approach to calculating eigenvalues and eigenvectors. You only need to know how to do the power method.
• Jan. 26, 2006 I added the review sheet for Midterm I. You can find this in the column to the left. Also, I added the new challenge assignment.
• Jan. 25, 2006 We looked at discrete dynamical systems, and how the eigenvalues and eigenvectors of a matrix can be used to describe the long term behaviour of a dynamical system. Know what is meant by saying that the origin is an attractor, repellor, or saddle point.
• Jan. 23, 2006 Today we finished our discussion of Section 5.5 on complex eigenvalues and eigenvectors. Know what is meant by the real and imaginary parts of a complex vectors, how eigenvalues and vectors appear as complex conjugates for matrices with real entries, and understand Theorem 9.
• Jan. 20, 2006 We finished up Section 5.4. We then started our discussion on complex eigenvalues and eigenvectors (this is the material of Section 5.5). You should be able to find complex eigenvalues and their associated eigenvectors.
• Jan. 18, 2006 Today we discussed section 5.4. You should know how given a linear transformation to form the matrix of this transformation relative to the two bases. Your first homework assignment was also due.
• Jan. 16, 2006 Class was cancelled again today because I could not get back to Thunder Bay on time.
• Jan. 13, 2006 Class is cancelled today since I have to go to a conference.
• Jan. 11, 2006 Today we finished the material of Section 5.3. After today's class, you should be able to determine if a matrix is diagonalizable, and if it is, you should be able to find the appropriate decomposition. I also gave out the first homework assignment.
• Jan. 9. 2006 We finished the material of Section 5.2 on the characteristic equation. You should know what it means for a two matrices to be similar. We also started Section 5.3 on diagonalization. You should know what it means for a matrix to be diagonalizable, and how to determine if a matrix is diagonalizable.
• Jan. 6, 2006 Today we finished the material of Section 5.1. We also started Section 5.2 on the characteristic equation. Know what a characteristic equation is, and how to use it to find the eigenvalues of a matrix.
• Jan. 5, 2006 The classroom has been moved to RB 2047.
• Jan. 4, 2006 Welcome Back! For our first class, I handed out the course information sheet (you can find a link to this sheet on this page). I also gave our first lecture on Section 5.1. You should know what a eigenvector, eigenvalue, and eigenspace is by the end of today's lecture.
• Dec. 6, 2005 I set up the webpage.