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MATH 221: Linear Algebra

2020 Fall, Emory University


Contacts

Lecture Instructor Dr. Le Chen
Email le.chen@emory.edu
Office Math & Science Center - E431
Office hours Tue-Thur, 4:00pm -- 5:00pm, or by appointments.
Zoom Classroom Click here (password on Canvas page).
Lab Instructors Michael Cerchia Zitong Pei
Email michael.cerchia@emory.edu zitong.pei@emory.edu
Sections 7/8 5/6
Sections Class meeting (Tue+Thur) Lab (Friday) Lab Instructor
Math221-5 1:00PM - 2:15PM 12:00PM - 12:50PM Zitong Pei
Math221-6 1:00PM - 2:15PM 1:00PM - 1:50PM Zitong Pei
Math221-7 2:30PM - 3:45PM 2:00PM - 2:50PM Michael Cerchia
Math221-8 2:30PM - 3:45PM 3:00PM - 3:50PM Michael Cerchia

Course description

(Image from Wikipedia)

Linear algebra is a branch of mathematics concerning linear equations such as \(a_1 x_1 + \cdots + a_n x_n = b\), linear maps such as \((x_1,\cdots,x_n) \mapsto a_1x_1 + \cdots + a_n x_n\), and their representations in vector spaces and through matrices. Linear algebra is central to almost all areas of mathematics. It is also used in most sciences and engineering areas.

This course begins with the definition of a matrix and some fundamental operations that can be performed on matrices, such as adding or multiplying two matrices together. Vector spaces are also introduced. A connection is then formed by modeling vector spaces using matrices. Advanced topics involving matrices, such as diagonalization and quadratic forms, eigenvalues and eigenvectors, orthogonalization, and the Gram-Schmidt process are examined. At the end of the class, you will understand how google ranks web pages.

Textbook

We will use the following online book which is free to download:

Coverage

The book consists of eleven chapters, we will cover most parts of the first eight chapters:

Prerequisite

Learning outcomes

By the end of this course, students will be able to

Students obligations

In order to successfully master the material and complete the course, you are expected to


Note: The syllabus was created in May 2020, and it is subject to changes during the semester.


Homework

Midterm tests

Due dates for homework and tests

Final exams

Attendance

Assessment


Text and slides

Chapter/Section Text Slides Slides
Chapter 1. Systems of Linear Equations text    
Section 1-1. Solutions and Elementary Operations text presentation handout
Section 1-2. Gaussian Elimination text presentation handout
Section 1-3. Homogeneous Equations text presentation handout
Section 1-4. An Application to Network Flow text presentation handout
Section 1-5. An Application to Electrical Network text presentation handout
Section 1-6. An Application to Chemical Reactions text presentation handout
Section 1-S. Supplementary Exercises for Chapter 1 text presentation handout
Chapter 2. Matrix Algebra text    
Section 2-1. Matrix Addition and Scalar Multiplication and Transportation text presentation handout
Section 2-2. Matrix-Vector Multiplication text presentation handout
Section 2-3. Matrix Multiplication text presentation handout
Section 2-4. Matrix Inverses text presentation handout
Section 2-5. Elementary Matrices text presentation handout
Section 2-6. Linear Transformations text presentation handout
Section 2-7. LU-Factorization text presentation handout
Section 2-8. An Application to Input-Output Economic Model text presentation handout
Section 2-9. An application to Markov Chains text presentation handout
Section 2-S. Supplementary Exercises for Chapter 2 text presentation handout
Chapter 3. Determinants and Diagonalization text    
Section 3-1. The Cofactor Expansion text presentation handout
Section 3-2. Determinants and Matrix Inverses text presentation handout
Section 3-3. Diagonalization and Eigenvalues text presentation handout
Section 3-4. An Application to Linear Recurrences text presentation handout
Section 3-5. An Application to Systems of Differential Euqations text presentation handout
Section 3-6. Proof of the Cofactor Expansion Theorem text presentation handout
Section 3-S. Supplementary Exercises for Chapter 3 text presentation handout
Chapter 4. Vector Geometry text    
Section 4-1. Vectors and Lines text presentation handout
Section 4-2. Projections and Planes text presentation handout
Section 4-3. More on the Cross Product text presentation handout
Section 4-4. Linear Operators on R3 text presentation handout
Section 4-5. An Application to Computer Graphics text presentation handout
Section 4-S. Supplementary Exercises for Chapter 4 text presentation handout
Chapter 5. Vector Space Rn text    
Section 5-1. Subspaces and Spanning text presentation handout
Section 5-2. Independent and Dimension text presentation handout
Section 5-3. Orthogonality text presentation handout
Section 5-4. Rank of a Matrix text presentation handout
Section 5-5. Similarity and Diagonalization text presentation handout
Section 5-6. Best Approximation and Least Squares text presentation handout
Section 5-7. An Application to Correlation and Variance text presentation handout
Section 5-S. Supplementary Exercises for Chapter 5 text presentation handout
Chapter 6. Vector Spaces text    
Section 6-1. Examples and Basic Properties text presentation handout
Section 6-2. Subspaces and Spanning Sets text presentation handout
Section 6-3. Linear Independence and Dimensions text presentation handout
Section 6-4. Finite Dimensional Spaces text presentation handout
Section 6-5. An Application to Polynomials text presentation handout
Section 6-6. An Application to Differential Equations text presentation handout
Section 6-S. Supplementary Exercises for Chapter 6 text presentation handout
Chapter 7. Linear Transformations text    
Section 7-1. Examples and Elementary Properties text presentation handout
Section 7-2. Kernel and Image of a Linear Transformation text presentation handout
Section 7-3. Isomorphisms and Composition text presentation handout
Section 7-4. A Theorem about Differential Equations text presentation handout
Section 7-5. More on Linear Recurrences text presentation handout
Chapter 8. Orthogonality text    
Section 8-1. Orthogonal Complements and Projections text presentation handout
Section 8-2. Orthogonal Diagonalization text presentation handout
Section 8-3. Positive Definite Matrices text presentation handout
Section 8-4. QR-Factorization text presentation handout
Section 8-5. Computing Eigenvalues text presentation handout
Section 8-6. The Singular Value Decomposition text presentation handout
Section 8-7. Complex Matrices text presentation handout
Section 8-8. An Application to Linear Codes over Finite Fields text presentation handout
Section 8-9. An Application to Quadratic Forms text presentation handout
Section 8-10. An Application to Constrained Optimization text presentation handout
Section 8-11. An Application to Statistical Principal Component Analysis text presentation handout

Tentative schedule


Gradescope


Netiquette

Not all forms of communication found online are appropriate for an academic community or respectful of others. In this course (and in your professional life that follows), you should practice appropriate etiquette online (``netiquette''). Here are some guidelines:

Honor code

Accessibility

Your success in this class is important to me. We will all need accommodations because we all learn differently. If there are aspects of this course that prevent you from learning or exclude you, please let me know as soon as possible. Together we’ll develop strategies to meet both your needs and the requirements of the course.

I encourage you to visit the Office of Accessibility Services (OAS) to determine how you could improve your learning as well. You can register and make a request for services from OAS. In this case, please do inform me of such requests. See the following link for more information:

Harassment

Discriminatory harassment of any kind, whether it is sexual harassment or harassment on
the basis of race, color, religion, ethnic or national origin, gender, genetic
information, age, disability, sexual orientation, gender identity, gender expression,
veteran’s status, or any factor that is a prohibited consideration under applicable law,
by any member of the faculty, staff, administration, student body, a vendor, a contractor,
guest or patron on campus, is prohibited at Emory.
  1. Why study linear algebra?
  2. Fun Linear Algebra Problems
  3. An Intuitive Guide to Linear Algebra
  4. The $25,000,000,000 eigenvectorthe linear algebra behind Google

Acknowledgement


© Le Chen, Emory, 2020.