**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 **
e-mail:** costin.10

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

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).

Homework 3 due Friday Sept 20

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

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.

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

Mon Oct 21 Notes

Wed Oct 23 Notes

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

Mon Nov 4 Notes

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

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

Notes

Fri Nov 15 The full chapter on

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

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: