Linear Algebra III: Determinants and Eigenvalues

Learners: 150

Instructor: Greg Mayer

Duration: 6.00

This course introduces students to the concept of determinants and eigenvalues. It covers the invertibility criterion for a square matrix, the Cramer's rule, and the eigenvalue problem. Students will learn how to calculate the determinant of a matrix and how to use it to solve linear systems. They will also explore the properties of eigenvalues and eigenvectors. ▼▲

Course Feature Course Overview Course Provider Discussion and Reviews

Go to class

Course Feature

Cost:

Free

Provider:

Edx

Certificate:

Paid Certification

Language:

English

Start Date:

17th Aug, 2026

Course Overview

❗The content presented here is sourced directly from Edx platform. For comprehensive course details, including enrollment information, simply click on the 'Go to class' link on our website.

Updated in [March 06th, 2023]

Unlock the Exciting World of Learning! Here's What Awaits You: With Linear Algebra III: Determinants and Eigenvalues, you will gain a comprehensive understanding of the determinant and its applications, as well as the eigenvalues and eigenvectors of a linear transformation. You will learn how to apply an invertibility criterion for a square matrix, measure the amount by which a linear transformation changes the area of a region, and decompose the action of a linear transformation. These concepts are essential for computer graphics, multivariable calculus, and other advanced courses. With this course, you will be well-equipped to tackle the challenges of the modern world.

[Applications]
Upon completion of this course, students will be able to apply the concepts of determinants and eigenvalues to a variety of applications. These applications include understanding invertibility criteria for square matrices, measuring the amount by which a linear transformation changes the area of a region, and decomposing the action of a linear transformation. These concepts are useful in computer graphics, multivariable calculus, discrete dynamical systems, and other areas of industry, science, engineering, and mathematics.

[Career Paths]
1. Data Scientist: Data Scientists use linear algebra to analyze large datasets and uncover patterns and trends. They use eigenvalues and eigenvectors to identify the most important features of a dataset and to reduce the dimensionality of the data. As data science becomes increasingly important in industry, the demand for data scientists is growing rapidly.

2. Machine Learning Engineer: Machine Learning Engineers use linear algebra to develop algorithms that can learn from data. They use eigenvalues and eigenvectors to identify the most important features of a dataset and to reduce the dimensionality of the data. As machine learning becomes increasingly important in industry, the demand for machine learning engineers is growing rapidly.

3. Computer Graphics Engineer: Computer Graphics Engineers use linear algebra to create realistic 3D images and animations. They use determinants to measure the amount by which a linear transformation changes the area of a region. As computer graphics become increasingly important in industry, the demand for computer graphics engineers is growing rapidly.

4. Financial Analyst: Financial Analysts use linear algebra to analyze financial data and make predictions. They use eigenvalues and eigenvectors to identify the most important features of a dataset and to reduce the dimensionality of the data. As financial analysis becomes increasingly important in industry, the demand for financial analysts is growing rapidly.

[Education Paths]
1. Bachelor of Science in Mathematics: A Bachelor of Science in Mathematics is a degree program that focuses on the study of mathematics and its applications. This degree program typically includes courses in calculus, linear algebra, abstract algebra, and statistics. Students in this program will also learn about the history of mathematics and its applications in various fields. This degree program is ideal for those who want to pursue a career in mathematics or related fields.

2. Master of Science in Applied Mathematics: A Master of Science in Applied Mathematics is a degree program that focuses on the application of mathematics to solve real-world problems. This degree program typically includes courses in calculus, linear algebra, numerical analysis, and optimization. Students in this program will also learn about the application of mathematics in various fields such as engineering, finance, and economics. This degree program is ideal for those who want to pursue a career in applied mathematics or related fields.

3. Doctor of Philosophy in Mathematics: A Doctor of Philosophy in Mathematics is a degree program that focuses on the advanced study of mathematics and its applications. This degree program typically includes courses in algebra, analysis, geometry, and topology. Students in this program will also learn about the history of mathematics and its applications in various fields. This degree program is ideal for those who want to pursue a career in mathematics or related fields.

4. Master of Science in Data Science: A Master of Science in Data Science is a degree program that focuses on the application of mathematics, statistics, and computer science to solve real-world problems. This degree program typically includes courses in calculus, linear algebra, machine learning, and data mining. Students in this program will also learn about the application of data science in various fields such as healthcare, finance, and marketing. This degree program is ideal for those who want to pursue a career in data science or related fields.