**MATHEMATICS 5101: ****Linear Mathematics in Finite Dimensions**

Information for the section at 9:10 of AU 2017,
Enarson Classroom Bldg 358

**Instructor:** Dr. Rodica
D. Costin

**Office:** 436 Math Tower

**Office hours: **
MW 10:20-11:15 AM or by
appointment

** e-mail:** costin.10

I will post here lecture notes, as well as homework assignments and other announcements.

Wed Aug 23 We went over
Sec.1.1 and 1.2 in the lecture notes 1.**Vector Spaces**.

Fri Aug 25 We continued from the notes above**: Sec. 1.3**

Mon Aug 28 You are
responsible for reviewing complex numbers (operations, polar
form, geometric interpretation, the n'th
roots of 1)

**Exercise:** (you do not need to turn it in, but we will
use these facts)

1. Show that any n'th
root of 1 (that is, a number z so that z^n=1)
has the form exp(2 pi k i/n)
for k integer.

2. Denote a=exp(2
pi i/n). Show that 1, a, a^2,..., a^(n-1) are all the roots of 1
(that is, there are n of them, and no more).

3. Show that the number a above satisfies
1+a+a^2+...+a^(n-1)=0

4. Plot, on separate planes, the roots of 1 for
n=2. Then for n=3, then n=4. Then n=5. What do you see?

Wed Aug 30
We started Sec. 2.2.

HW 1 due Wed Sept 6

Fri Sept 1st We
finished the chapter on Vector Spaces.

Wed Sept 6 We start
talking about determinants. Here are the lecture notes: **2.
Determinants** (new
file)

Here is a Maple example on how to
solve systems and produce latex output.

HW 2 due
Wed Sept 13.

Fri Sept 8 We continued determinants (Sec. 2.4 and 2.5)
with a brief break for a fire alarm.

Mon Sept 11 We finished determinants and started **3.
Linear Transformations**.

Wed Sept 13 We did Sec. 2.2 and 2.3 (of Linear
Transformations).

Here is **HW3** due Wed Sept 20.

Fri Sept 14 Null space and range. Here is the edited chapter on linear
transformations, with changes in Sec. 3.5.

Mon Sept 18 We did Sec. 3.6, 3.7.

Wed Sept 20
We did Sec. 3.8, 3.9.1. Here is **HW4**

Fri Sept 22 We
continued...

Mon Sept 25 and
continued... with Sec. 3.11

Wed Sept 27 Here is a
handout and **HW 5 .
**We will soon start the chapter on

Fri Sept 29 We finished Ch. 3 and started Ch.4, on Eigenvalues and Eigenvectors, Sec. 4.3

Mon Oct 2 We continued with Sec. 4.2, 4.4...up to 4.12.

Wed Oct 4 We continued with 4.1.13, 4.1.14 (but did not go over Remark 1. points 3. and 4.)

Here is the chapter on

Fri Oct 6 Sec 14.14, 15

Mon Oct 9 We proved that similar matrices have the same characteristic polynomial and we did a review.

**MIDTERM: Wednesday Oct. 11. You
are allowed to bring a cheat sheet (regular size paper
with your own notes, written on both sides, if you wish).** Required material: everything!

**Topics not to be missed when you
review:** examples of
vector spaces that we often encountered, linear
transformations (definition, null space, range, theorems and
other facts, inverse, right and left inverse, important
examples). *Eigenvectors and eigenvalues *(definition,
calculation, theorems and other facts, application to
differential equations).** **

**Wednesday Oct. 11** Midterm!

Have a Nice Break!

Mon Oct 16
We showed that det(AB)=det A det
B, here are the notes. And 4.14.
1...3.

Wed Oct 18 Here is **HW7. **We
did 14.6.: 3, 4, 14.7, 5.1, 5.2

Fri Oct 20 We covered 5.3

Mon Oct 23 We covered 5.4, 5.6

Wed Oct 25 **HW8** We covered 5.6.1 and 2, also 5.8

Fri Oct 27 plan: 5.9, 5.10-12, 6.2.7, 6.3
then** ****Inner Product
Spaces**

Mon Oct 30 we continued...

Wed Nov 1 and continued up
to page 10. Here is **HW 9.**

Fri Nov 3 and continued

Mon Nov 6 and continued up to Sec.
8.1

Wed Nov 8 we continued with 8.2,8.3 and 11.1. Here is **HW 10.
Selfadjoint transformations
**

Mon Nov 13 and continued with Sec. 11.2-3, 11.5-6

Wed Nov 15 Sec 11.7, 11.9-11, 12.1.1. And here is next HW, due Wed Nov 29,Fri Nov 17 We continued up to 12.3.

Mon Nov 20 We continued up to 12.7

Happy Thanksgiving!

Mon Nov 27 continued with...

Fri Dec 1

Mon Dec 4

Wed Dec 6 Review

Final exam: Monday
Dec
11 10:00am-11:45am according to the
university
schedule (please check!)

**Other references:**