MATHEMATICS 5101: Linear Mathematics in Finite Dimensions

Information for the section at 4:10 of AU 2013

Lecture CH 0312 MWF 4:10-5:05 Costin, Rodica

Instructor: Dr. Rodica D. Costin
Office: 436 Math Tower
Office hours: Wed 12-1p.m., (new time!)
                       Fri: 1:30-2:30 p.m.,
                       or by appointment

General information


Here are lecture notes for the first few lectures:

Vector Spaces

Wed Aug 21 We start by giving the abstract definition of a vector space, Sec. 1.1 and 1.2 in the lecture notes Vector Spaces.

Fri Aug 23 We continued and followed up to Theorem 15.

Mon Aug 26 We went up to Theorem 20. Here is the revised chapter on Vector Spaces (typos corrected etc.)

Wed Aug 28 We finished the first chapter, and started to talk about Linear Transformations; here are the notes.

Linear Transformations

Homework 1 is due next Friday, Sept. 6.
(The grader will grade a subset of these problems and give points for turning in solutions for the others.)

Fri Aug 30 Lecture notes (with revised p.1-5).

Mon Sept 2  Labor

Wed Sept 4 Lecture notes (with revised pages, starting with p.8)

Homework 2 due Friday Sept 13.  A few first steps to help you do calculations using Maple.

Fri Sept 6 Lecture notes (with corrections and a change in notation)

Mon Sept 9 Lecture notes (we went through pages 16-21)

Wed Sept 11 We continue from the notes posted on Monday: left and right inverse and start talking about the Dual Space (see revised notes below).

The Dual Space

Homework 3 due Friday Sept 20

Fri Sept 13 ..continued

Mon Sept 16...continued.. here are revised pages 8-10 on the transpose

Eigenvalues and Eigenvectors

Wed Sept 18 We started the chapter on eigenvalues and eigenvectors. Here are the notes for today and for Friday.

Homework 4 due Friday Sept 27

The Wednesday office hour will be moved permanently from noon to 1p.m.

Office hours: Wed 12-1p.m., (new time!)
                       Fri: 1:30-2:30 p.m.,
                       or by appointment

Fri Sept 20 ...continued

Mon Sept 23 Lecture notes (pages 13-15 only, disregard pages 16-20)

Wed Sept 25 Lecture notes (with pages 16 and up revised)

Homework 5 due Friday Oct 4

Fri Sept 27 Lecture notes (with p 20, 21 revised)

Midterm exam: Friday Oct. 11

Mon Sept 30... we continued (see the lecture note of Friday Sept 27, Sec. 3.1, 3.2)

Homework 6
due Wednesday Oct. 9th! (OK, you can turn it in on Friday Oct 11 if need be, but it is better to have it done before, in preparation for the midterm exam. Look on the rest of the  problems of 5.2 also.)

Wed Oct 2 Lecture notes

Fri Oct 4

Mon Oct 7  Eigenvalues and Eigenvectors - full chapter

Wed Oct 9

Fri Oct 11 Midterm exam

Homework 7: (due Friday Oct 18) From the hand out of Oct 11, solve 5.3.3, 5.3.4, 5.3.7, 5.3.8, and 5.3.17-Typo here: the element (2,2) is not 5, but 0.5!!! (For this last problem you are supposed to check the formula of .16, that (I-A)(I+A+A^2+...)=I, valid when all eigenvalues of A have absolute value less than 1, as it is the case for A=number).

Inner product spaces

Mon Oct 14 Definition of inner product spaces Notes   (disregard page 6 here)

Wed Oct 16 Notes (with p 6 revised) (disregard page 10 and up here)

Homework 8 CORRECTION: in Problem 1, <x,y>=1/4 times the sum

Fri Oct 18 Notes

Oct 21 Notes

Wed Oct 23 Notes

Homework 9

Here is the full chapter on Inner Product Spaces.

Fri Oct 25 We started the chapter on Spectral Properties of Self-Adjoint Matrices Notes

Mon Oct 28  Rado lecture

Wed Oct 30 Notes

Homework 10

Fri Nov 1 Notes

Mon Nov 4   Notes

Wed Nov 6 Notes disregard pages 30 and up here, they are revised below

Homework 11

Fri Nov 8 Notes  please disregard p. 34 here, see it revised with the next lecture notes

Mon Nov 11 Veterans day (no classes)

Wed Nov 13    SDV
Application of SVD: image compression


Homework 12

Fri Nov 15  The full chapter on Spectral Properties of Self-Adjoint Matrices (with p 38 revised)
We started Functional Calculus

Mon Nov 18  ...Functional Calculus continued

Wed Nov 20  Normed Spaces

Fri Nov 22 ...continued. More on Lower Rank Approximations

Mon Nov 25 An introduction to linear mathematics in infinite dimensions. Some old Notes.

Nov 27-29     Happy Thanksgiving!  

Mon Dec 2

Final exam information official schedule .

Pick your the final exam in my office MW 436 on Monday Dec 9 between 2-3 p.m. in my office MW 436.

According to the official schedule the final exam is to be turned in on Tuesday Dec 10 between 4:00pm-5:45pm, in my office.

Other references:

Gilbert Strang's lectures