**4450.001/5500.001, Spring 2006
Matrix Theory
Conley**

the University of North Texas. |

**Instructor:** Charles Conley, GAB 419, (940)
565-3326

**Office hours:** MW 1-2, TR 12-1

**Class meets:** MWF 11:00-11:50, GAB 204

**Exams, homework, and grading:** There will be
two 100
point
midterms and a comprehensive 180 point final. There will be
thirteen homeworks totalling 120 points. They are worth 10
points
each and will be due at the beginning of
class each Friday (excepting exam weeks), except that the first two are
worth only 5 points and the first is due the first Monday of class (see
below). There will be no make-up
exams and late homework will be worth
half-credit.

**Text and prerequisites: **The text
is * Introduction to
Linear Algebra,* 3rd edition, by Gilbert Strang. The
prerequisite is Linear Algebra (2700 or its equivalent).

**Topics: **Our central goal is the spectral
theorem, which
states that a real symmetric matrix has an orthonormal basis of
eigenvectors. We will work through Chapters 1-6 of the text,
adding a few sections of Chapter 7 if there is time. There
will
be some overlap with the material from Math 2700, which we will review
and cover in greater depth.

Math 5500:
This is the
graduate version of 4450. The problem sets and exams for 5500
will contain additional problems emphasizing proofs.

Final Exam: Wednesday, May 10, 10:30-12:30

Homework 13, due Friday, May 5:

Section 7.3: 1-7

Section 7.4: 1-13, 20

5500 problems: 7.4: 15, 16, 23, 25

Homework 12, due Friday, April 28:

Section 7.1: 3, 4, 6, 12d, 13-15, 17, 18

Section 7.2: 1, 2, 4a, 5, 6, 11, 12, 21-23, 27

5500 problems: 7.1: 16, 19; 7.2: 24

Homework 11, due Friday, April 21:

Section 6.6: 1-8, 10, 12, 13, 15, 17, 20, 21

Section 6.7: 1-5, 7, 9, 10, 12

5500 problems: 6.6: 16, 18, 19; 6.7: 13, 15, 16

Homework 10, due Friday, April 14:

Section 6.4: 1-8, 11b, 16, 17, 21, 26

Section 6.5: 1ab, 2a, 3, 4, 10, 12a, 14a, 15, 18, 19 (assume A symmetric), 22, 25b, 26b

5500 problems: 6.4: 22, 23; 6.5: 16, 17, 20

Exam 2: Wednesday, April 5

Homework 9, due Friday, March 31:

Section 6.1: 16, 18, 19 (find the quantity in the three cases where it is possible), 20-22, 25, 26 (proof), 28, 30

Section 6.2: 1-8, 15-18, 22, 27, 29, 31, 36, 37

5500 problems: 6.1: 32, 34, 36; 6.2: 26, 30, 34, 40

Homework 8, due Friday, March 24:

Section 5.2: 4, 7, 8, 14, 15, 19, 20, 25

Section 5.3: 4, 5, 6b, 7, 10, 13, 15, 21

Section 6.1: 2-7, 9, 12, 14*

5500 problems: 5.2.10, 5.3.11-12, 6.1.11

Homework 7, due Friday, March 10:

Section 4.2: 1a, 3a, 5, 7, 11, 12, 13, 17

Section 4.4: 1, 3b, 12a, 14, 15ab, 18, 23

Section 5.1: 2, 3, 6, 8a, 10, 11, 18, 19, 28

5500 problems: 4.2: 19; 4.4: 25, 34; 5.1: 25, 26, 29

Homework 6, due Friday, March 3:

Section 3.5: 5, 13, 15, 17, 20, 23 (proof), 27 (proof), 28, 31, 32, 38

Section 3.6: 3, 5, 7, 8, 13, 15, 25

Section 4.1: 3, 11, 17, 24, 26, 29

5500 problems: 3.5.35, 3.5.39, 3.6.22, 3.6.29

Exam 1: Wednesday, February
22

Homework 5, due Friday, February 17:

Section 3.1: 4, 5b, 10, 15c, 17-19, 22, 26-29 (give proofs for 18 and 27)

Section 3.2: 1, 5b, 7b, 11a, 12a, 21, 23, 27

Section 3.3: 2b, 6, 10, 17a, 19, 22, 26, 27

Extra 5500 problems will be passed out in class

Homework 4, due Friday, February 10:

Section 2.5: 26, 34-36

Section 2.6: 3, 5, 7, 8a, 11, 13, 18, 19, 21, 26

Section 2.7: 3, 7, 16, 17, 19, 22, 24, 35-39

Extra 5500 problems will be passed out in class

Section 2.3: 3, 4, 11, 15, 17, 21, 23,
27, 28

Section 2.4: 6, 14, 16, 20-22, 35, 39

Section 2.5: 5-9, 13, 15, 25, 28

Extra problems for 5500 students will be announced on
Monday. (Warning
re 5500 extra problem 2b: it is too hard! Replace "prove that
n
is a power of 2" with "prove that n is divisible by 4". You
might
also like to try the following (not required): prove that if n is a
power of two, then such a matrix does exist .)

Homework 2, due Friday, January 27 (5 points):

Section 2.1: 4, 6, 8, 13, 18, 20, 22

Section 2.2: 7, 10, 12, 15, 19, 21-23

Homework 1, due Monday, January 23 (5 points):

Section 1.1: 3, 5, 14, 26

Section 1.2: 4, 6b, 8, 13, 20, 24, 29