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Determinants and Eigenvalues

Massive Open Online Course
  • Overview
  • Course Content
  • Requirements & Materials
Overview

Determinants and Eigenvalues

Course Description

At the beginning of this course we introduce the determinant, which yields two important concepts that you will use in this course. First, you will be able to apply an invertibility criterion for a square matrix that plays a pivotal role in, for example, the understanding of eigenvalues. You will also use the determinant to measure the amount by which a linear transformation changes the area of a region. This idea plays a critical role in computer graphics and in other more advanced courses, such as multivariable calculus.

This course then moves on to eigenvalues and eigenvectors. The goal of this part of the course is to decompose the action of a linear transformation that may be visualized. The main applications described here are to discrete dynamical systems, including Markov chains. However, the basic concepts— eigenvectors and eigenvalues—are useful throughout industry, science, engineering, and mathematics.

Prospective learners enrolling in this course are encouraged to first complete the linear equations and matrix algebra courses before starting this class.

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Course Content

INTRODUCTION TO DETERMINANTS

PROPERTIES OF THE DETERMINANT

VOLUME AND LINEAR TRANSFORMATIONS

MARKOV CHAINS

EIGENVALUES AND EIGENVECTORS

THE CHARACTERISTIC EQUATION

DIAGONALIZATION

COMPLEX EIGENVALUES

GOOGLE PAGE RANK

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Requirements & Materials
Prerequisites

Recommended

  • High school algebra, geometry, and pre-calculus

Required

  • Linear Equations (DL 0050M)

  • Matrix Algebra (DL 0051M)

Materials

Required

  • Internet connection (DSL, LAN, or cable connection desirable)
  • Adobe Acrobat PDF reader (to download for free, visit get.adobe.com/reader/)
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Who Should Attend

This course is designed for undergraduate students, advanced high school students, who are interested in pursuing any career path or degree program that involves linear algebra, or industry employees who are seeking a better understanding of linear algebra for their career development.

Computing professional working on laptop computer

What You Will Learn

  • How to compute determinants of using cofactor expansions and properties of determinants
  • Compute areas and volumes of regions in Rn under a given linear transformation using determinants
  • Real-world problems using Markov chains
  • The characteristic polynomial to compute eigenvalues of a matrix
  • Eigenvalues and the corresponding eigenspaces for a matrix
  • The invertibility of a matrix using determinants and eigenvalues
  • How to decompose matrices into a product of matrices by using a matrix factorization
  • Eigenvalues to determine identify the rotation and dilation of a linear transform
  • How to construct the Google matrix for web and compute its Google PageRank
Adult learners collaborating in classroom

How You Will Benefit

  • Apply theorems related to eigenvalues to characterize the invertibility of a matrix.
  • Apply theorems to characterize matrices with complex eigenvalues.
  • Apply matrix powers and theorems to characterize the long-term behavior of a Markov chain.
  • Construct a transition matrix, a Markov Chain, and a Google Matrix for a given web, and compute the PageRank of the web.
  • Analyze mathematical statements and expressions involving linear systems and matrices. For example, to describe matrices in terms of diagonalizability and their eigenvectors.
  • Taught by Experts in the Field
  • Grow Your Professional Network
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The course schedule was well-structured with a mix of lectures, class discussions, and hands-on exercises led by knowledgeable and engaging instructors.

- Abe Kani
President

Frequently Asked Questions

Policies
Access (ADA)

The Georgia Tech Global Learning center is compliant under the Americans with Disabilities Act. Any individual who requires accommodation for participation in any course offered by GTPE should contact us prior to the start of the course.

Assessment

Courses that are part of certificate programs include a required assessment. Passing criteria is determined by the instructor and is provided to learners at the start of the course.

Attendance

CEUs are awarded to participants who attend a minimum of 80% of the scheduled class time.

Citizenship

Georgia Tech’s Office of Research Security and Compliance requires citizenship information be maintained for those participating in most GTPE courses. Citizenship information is obtained directly from the learner at the time of registration and is maintained in the Georgia Tech Student System.

Course Cancellations

GTPE reserves the right to substitute instructors, change course dates and locations, or cancel a course due to insufficient enrollment or unforeseen events. If GTPE cancels a course, participants will be notified via email or phone and will be given the option for a full refund or to transfer their registration and any fees paid to another course. It is the responsibility of the student to pay any difference in price, if applicable, when a transfer is made.  GTPE is not responsible for nonrefundable plane tickets, hotel and rental car deposits, nor any other expenses incurred.

Data Collection and Storage

Participants in GTPE courses are required to complete an online profile that meets the requirements of Georgia Tech Research Security. Information collected is maintained in the Georgia Tech Student System. The following data elements are considered directory information and are collected from each participant as part of the registration and profile setup process:

  • Full legal name
  • Email address
  • Shipping address
  • Company name

This data is not published in Georgia Tech’s online directory system and therefore is not currently available to the general public. Learner information is used only as described in our Privacy Policy. GTPE data is not sold or provided to external entities.

Sensitive Data
The following data elements, if in the Georgia Tech Student Systems, are considered sensitive information and are only available to Georgia Tech employees with a business need-to-know:

  • Georgia Tech ID
  • Date of birth
  • Citizenship
  • Gender
  • Ethnicity
  • Religious preferences
  • Social security numbers
  • Registration information
  • Class schedules
  • Attendance records
  • Academic history

At any time, you can remove your consent to marketing emails as well as request to delete your personal data. Visit our GTPE EU GDPR page for more information.

Inclement Weather

Classes and events being held at the Georgia Tech Global Learning Center in Atlanta may be impacted by closures or delays due to inclement weather. The Georgia Tech Global Learning Center will follow the guidelines of Georgia Tech main campus in Atlanta.

Students, guests, and instructors should check the Georgia Tech homepage for information regarding university closings or delayed openings due to inclement weather. Please be advised that if campus is closed for any reasons, all classroom courses are also cancelled

Program Completion

GTPE certificates of program completion consist of a prescribed number of required and elective courses offered and completed at Georgia Tech within a consecutive six-year period. Exceptions, such as requests for substitutions or credit for prior education, can be requested through the petition form. Exceptions cannot be guaranteed.

Refunds

Withdrawals
Classroom courses
To receive a full refund, you must submit a withdrawal request 10 or more business days prior to the course start date. Final course grade will be a W. 

Online courses
To receive a full refund, you must submit a withdrawal request prior to the course start date and have not previously accessed the course. Final course grad will be a W. 

Substitutions
Course substitutions are allowed if for the same course and requested two or more business days prior to the start of the course. All substitution requests must be submitted via the GTPE Substitution Form. Substitutions cannot be guaranteed for classified, restricted, or approval-required courses.

Transfers
Course transfers are allowed if requested 10 or more business days prior to the start of the course. All transfer requests must be submitted via the GTPE Transfer Form.

Smoking & Tobacco

Georgia Tech is a tobacco-free and smoke-free campus. The use of cigarettes, cigars, pipes, all forms of smokeless tobacco, and any other smoking devices that use tobacco are strictly prohibited. There are no designated smoking areas on campus.

Special Discounts

Courses that are eligible for special discounts will be noted accordingly on the course page. Only one coupon code can be entered during the checkout process and cannot be redeemed after checkout is complete. If you have already registered and forgot to use your coupon code, you can request an eligible refund. GTPE will cancel any transaction where a coupon was misused or ineligible. If you are unsure if you can use your coupon code, please check with the course administrator.

GTPE does not have a program for senior citizens. However, Georgia Tech offers a 62 or Older Program for Georgia residents who are 62 or older and are interested in taking for credit courses. This program does not pay for noncredit professional education courses. Visit the Georgia Tech Undergraduate Admissions page for more information on the undergraduate program and Georgia Tech Graduate Admissions page for more information on the graduate program.

Enrollment
How do MOOCs work?

Designed for an online audience, MOOCs are available to anyone with an internet connection and are free to enroll. Some MOOCs can be started any time – others at regular intervals – and range in length from a few weeks to a few months to complete. You’ll have access to a wide range of online media and interactive tools, including video lectures, class exercises, discussions, and assessments.

Who can enroll in MOOCs?

Anyone with an internet connection can enroll. Sme courses may be unavailable in a small number of countries because of trade restrictions or government policies.

How do you enroll in a MOOC?

Visit one of our partner platforms — edX, Coursera, or Udacity — to enroll in a MOOC. Then, watch the pre-recorded lectures, learn from the course readings, and complete related work, like quizzes and in some cases, final projects.

How much do MOOCs cost?

Most courses are free, though there is a small fee if you opt to work towards a certificate of completion. Some courses count toward university credit—and some, like our online master’s program in computer science, offer a full degree. These credit-bearing courses do have fees and applications associated with them.

MOOC Credentials
Can I receive CEUs from completed a MOOC?

Yes, Georgia Tech offers CEUs for some completed MOOC courses taken through Coursera and edX. You have the option of purchasing CEUs after earning a verified course certificate.

What is a digital badge?

A digital badge is an acknowledgement that you've successfully completed a MOOC course. You can display your digital badge on your online profiles so that colleagues and employers can see your achievements at a glance.

What other credentials are available after completing a MOOC?

You can earn CEUs, digital badges, and verified certificates of completion. You can also use MOOCs as an alternate pathway to enter Georgia Tech master's programs through The Analytics: Essential Tools and Methods MicroMasters and the Online Master's in Computer Science.

Who issues the transcript or completion certification?

Certificates of completion are issued by the online providers edX, Coursera, and Udacity. Although they are a great way to showcase your skills, they are not the same as official academic credit from Georgia Tech. However, if you purchase CEUs (which are denoted by a badge), then you can request an official GTPE transcript for free.

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