# Matrix Methods Syllabus

## COURSE INFORMATION

**Course Description:** Matrices and matrix algebra,
determinants, systems of linear equations,

Gaussian elimination , eigenvalues and eigenvectors, linear transformation ,
applications in science

and engineering.

** Course Prerequisites : **Math 2414 or concurrent
enrollment

**Student Learning Outcomes:** Upon completion of this
course, students should be able to do the

following:

• Perform basic matrix operations including row reduction , transpose, finding
the inverse

and finding the determinant.

• Solve systems of linear equations using substitution, Gaussian elimination,
Cramers rule

and inverse matrices.

• Find eigenvalues and eigenvectors as well as understanding their properties
and importance

to matrix theory and applications.

• Understand the basic properties of Euclidean space including linear
independence, dimension,

rank, orthoganality, norm and projection.

## COURSE CONTENT

**Required Text:**

Bronson, Richard. Matrix Methods , An Introduction , 2nd edition, Academic Press,
1991.

ISBN: 978-0121352516

**List of Course Topics: **The following is a detailed
list of the sections from your textbook. Chapters

one through five will be covered in detail and selected topics will be chosen
from the remaining

chapters.

Chapter 1. Matrices

Section 1.1: Basic Concepts

Section 1.2: Operations

Section 1.3: Matrix Multiplication

Section 1.4: Special Matrices

Section 1.5: Submatrices and Partitioning

Section 1.6: Vectors

Section 1.7: The Geometry of Vectors

Chapter 2. Simultaneous Linear Equations

Section 2.1: Linear Systems

Section 2.2: Solutions by Substitution

Section 2.3: Gaussian Elimination

Section 2.4: Pivoting Strategies

Section 2.5: Linear Independence

Section 2.6: Rank

Section 2.7: Theory of Solutions

Chapter 3. The Inverse

Section 3.1: Introduction

Section 3.2: Calculating Inverses

Section 3.3: Simultaneous Equations

Section 3.4: Properties of the Inverse

Section 3.5: LU Decomposition

Chapter 4. Determinants

Section 4.1: Introduction

Section 4.2: Expansion by Cofactors

Section 4.3: Properties of Determinants

Section 4.4: Pivotal Condensation

Section 4.5: Inversion

Section 4.6: Cramer’ s Rule

Chapter 5. Eigenvalues and Eigenvectors

Section 5.1: Definitions

Section 5.2: Eigenvalues

Section 5.3: Eigenvectors

Section 5.4: Properties of Eigenvalues and Eigenvectors

Section 5.5: Linearly Independent Eigenvectors

Section 5.6: Power Methods

Chapter 6. Real Inner Products

Section 6.1: Introduction

Section 6.2: Orthonormal Vectors

Section 6.3: Projections and QR-Decomposition

Section 6.4: The QR-Algorithm

Section 6.5: Least- Squares

Chapter 7. Matrix Calculus

Section 7.1: Well-Defined Functions

Section 7.2: Cayley-Hamilton Theorems

Section 7.3: Polynomials of Matrices – Distinct Eigenvalues

Section 7.4: Polynomials of Matrices – General Case

Section 7.5: Functions of a Matrix

Section 7.6: The Function eAt

Section 7.7: Complex Eigenvalues

Section 7.8: Properties of eA

Section 7.9: Derivatives of a Matrix

## COURSE TIMELINE

**Tentative Schedule:** This schedule should give you a
rough idea of the pace of the course. Due to

the accelerated nature of summer courses , you will be expected to cover a great
deal of material

in each class, and content will build quickly. It is extremely important to stay
current with course

topics.

## COURSE EVALUATION

**Homework: **You will have assigned homework every
night. Due to the accelerated timeline of

the course and the amount of material to be covered, you MUST stay on top of
your homework in

order to succeed in this course. Homework will be collected two class days after
assigned unless

otherwise announced in class. For submission, fold homework lengthwise (into a
4” ×11”) and place

on the teaching podium BEFORE CLASS BEGINS. Late homework will not be accepted.

**In-Class Exams: **You will have three in-class exams,
tentatively scheduled for 22 July, 31 July,

and 12 August. As per the technology policy, no technological assistance will be
available during

exams.

**Final Exam:** You will have a comprehensive final
exam during the regularly scheduled class on

Friday, 14 August.

**Grading:** Grades will be computed as follows:

Homework and Quizzes 10% In-Class Exams 60 % Final Exam 30% |

IMPORTANT DATES

July 13 Classes begin July 16 Census Date July 31 Last day to drop or withdraw from a course or courses August 14 Final exams |

## INSTRUCTOR’S POLICIES

**Make-ups:** Make-ups for documented absences that are
required as part of a UT Tyler obligation

(e.g., athletes participating in an event, participation in a debate contest,
etc.) or for religious observation

will be granted. For all make-ups of this type, documentation and prior
notification of

at least one week are required. All other make-ups will be granted only in
extreme circumstances

and solely at Dr. Graves’s discretion.

**Technology Policy:** No calculators, PDAs, or
computers will be allowed on exams. Use of Mathematica

or other software may be helpful in checking homework answers, but credit will
only be

given for homework showing legible handwritten work.

## UNIVERSITY POLICIES

For University policies concerning Students’ Rights and
Responsibilities, Grade Replacement/Forgiveness,

State-Mandated Course Drop Policy, Disability Services, Student Absence due to
Religious Observance,

Student Absence for University-Sponsored Events and Activities, and the Social
Security

and FERPA Statement please see:

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