Linear Algebra III: Determinants and Eigenvalues

Greg Mayer, GTx

This course takes you through roughly three weeks of MATH 1554, Linear Algebra, as taught in the School of Mathematics at The Georgia Institute of Technology.

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

What will you learn

Upon completion of this course, learners will be able to:

  • Compute determinants of using cofactor expansions and properties of determinants
  • Compute the area of regions in R^3 under a given linear transformation using determinants
  • Model and solve real-world problems using Markov chains
  • Verify that a given vector is an eigenvector of a matrix
  • Verify that a scalar is an eigenvalue of a matrix
  • Construct an eigenspace for a matrix
  • Characterize the invertibility of a matrix using determinants and eigenvalues
  • Apply theorems related to eigenvalues (for example, to characterize the invertibility of a matrix)
  • Factorize 2 × 2 matrices that have complex eigenvalues
  • Use eigenvalues to determine identify the rotation and dilation of a linear transform
  • 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.

Dates:
  • 28 September 2020
Course properties:
  • Free:
  • Paid:
  • Certificate:
  • MOOC:
  • Video:
  • Audio:
  • Email-course:
  • Language: English Gb

Reviews

No reviews yet. Want to be the first?

Register to leave a review

Show?id=n3eliycplgk&bids=695438
NVIDIA
More from 'Mathematics, Statistics and Data Analysis':
B7b69de4-da99-4291-bc0f-e3b568d78237-b473275d5797.small Business Analytics for Data-Driven Decision Making
Learn how to lead your firm to make better business decisions using analytic...
52b6c2bf-2b08-4e7b-a7a5-faa2aa294d7e-3608f36e6e73.small Linear Algebra IV: Orthogonality & Symmetric Matrices and the SVD
This course takes you through roughly five weeks of MATH 1554, Linear Algebra...
7a7d4897-584a-4667-aeeb-c3a87a0cc15c-99186295b0b7.small Manufacturing Systems I
Learn about manufacturing systems and ways to analyze them in terms of material...
1e13fdc5-8cb9-4559-ab59-222ec1855d34-64c096e04a18.small Manufacturing Process Control II
Learn how to control process variation, including methods to design experiments...
03aa7c7e-cd4e-4b08-9beb-ab32fba5d947-902285399451.small Multidisciplinary Research methods for Engineers
Engineering is no longer limited to working in a single domain; nowadays engineers...
More from 'edX':
37041f86-a1df-4023-8dc8-6f0b2463dbaf-fd4f0c1d71f1.small Quantitative Biology Workshop
A workshop-style introduction to tools used in biological research. Discover...
D4c7cc7d-aa4a-4e74-849c-d17417e0a649-fa9c75a8bc1f.small Introduction to Management Information Systems (MIS): A Survival Guide
Gain the skills and knowledge needed to succeed in an MIS-dominated corporate...
14e5c2ce-e3bf-44a4-8c58-6ed05f717867-974da5bdc177.small English Composition
Learn to develop and express your ideas effectively for a variety of personal...
F5a5160a-9d43-4ac4-8779-0becc9da9337-3fa474c8c447.small Leading Digital and Data Decision Making
In this course, you will learn how leaders make managerial and relevant decisions...
B32a6606-e744-4935-90c7-07cf75d4be6b-dab694aadf88.small Future Trends of Fashion and Textiles 時尚之未來趨勢(時尚之未来趋势)
[中文介紹在英文介紹之後; 中文介绍在英文介绍之后] We intend to create this course as part of the management...

© 2013-2019