Linear Algebra II: Matrices and Linear Transformations from edX

A strong foundation in mathematics is critical for success in all science and engineering disciplines. Whether you want to make a strong start to a master’s degree, prepare for more advanced courses, solidify your knowledge in a professional context or simply brush up on fundamentals, this course will get you up to speed.

In many engineering master’s programs, you need to be familiar with linear algebra. This course will enable you to review the relevant topics.

This course focuses on matrices and linear transformations. Topics covered include matrix algebra, determinants, eigenvalues and eigenvectors, diagonalization and singular value decomposition. The course will help you refresh your knowledge, test your skills and review the relations between the many concepts in linear algebra.

The linear algebra courses within this series will offer you an overview of this branch of mathematics common to most engineering bachelor’s programs. They provide enough depth to cover the linear algebra you need to succeed in your engineering master’s/profession in areas such as computer graphics, systems and control, machine learning, quantum computing and more.

This is a review courseThis self-contained course is modular, so you do not need to follow the entire course if you wish to focus on a particular aspect. As a review course you are expected to have previously studied or be familiar with most of the material. Hence the pace will be higher than in an introductory course.

This format is ideal for refreshing your bachelor level mathematics and letting you practice as much as you want. Through the Grasple platform, you will have access to plenty of exercises and receive intelligent, personal and immediate feedback.

What's inside

Learning objectives

Perform algebraic operations on matrices such as matrix multiplication and matrix inversion.
Recognize linear transformations, apply their properties and find the standard matrix.
Find the determinant of a matrix and apply properties of determinants in the context of algebra and geometry.
Find eigenvalues, eigenvectors and eigenspaces of a matrix.

Diagonalize a matrix if possible and perform other similarity transformations.
Apply properties of symmetric matrices.
Find the singular value decomposition of a matrix.

Perform algebraic operations on matrices such as matrix multiplication and matrix inversion.
Recognize linear transformations, apply their properties and find the standard matrix.
Find the determinant of a matrix and apply properties of determinants in the context of algebra and geometry.
Find eigenvalues, eigenvectors and eigenspaces of a matrix.
Diagonalize a matrix if possible and perform other similarity transformations.
Apply properties of symmetric matrices.
Find the singular value decomposition of a matrix.

Syllabus

Week 1:

matrix multiplication and addition

matrix inversion

Week 2:

linear transformations

standard matrix of a linear transformation

examples of linear transformations in geometry

Week 3:

determinants

methods to find determinants

applications of determinants

Week 4:

eigenvalues and eigenvectors

eigenspaces

characteristic polynomials

complex eigenvalues

multiplicities of eigenvalues

Week 5:

diagonalization

similarity transformations

coordinate transformations

Week 6:

symmetric matrices

quadratic forms

singular value decomposition

Good to know

Know what's good

, what to watch for

, and possible dealbreakers

Helps learners refresh their linear algebra skills

Covers a wide range of topics such as matrices, transformations, and decompositions

Taught by qualified and experienced instructors

Provides flexibility with its modular format

Offers immediate feedback with its Grasple platform

Requires learners to have a prior understanding of linear algebra

Career center

Learners who complete Linear Algebra II: Matrices and Linear Transformations will develop knowledge and skills that may be useful to these careers:

Quantitative Analyst

Quantitative Analysts, also known as "Quants," are professionals who use mathematical and statistical methods to analyze financial data, identify trends, and develop trading strategies. The course "Linear Algebra II: Matrices and Linear Transformations" provides a strong foundation in linear algebra, which is essential for success in quantitative finance. The course covers topics such as matrix algebra, determinants, eigenvalues and eigenvectors, diagonalization, and singular value decomposition, which are all used extensively in financial modeling and analysis.

See salaries and explore the career path for Quantitative Analyst

Data Scientist

Data Scientists use scientific methods, processes, algorithms, and systems to extract knowledge and insights from data in various forms, both structured and unstructured. The course "Linear Algebra II: Matrices and Linear Transformations" provides a strong foundation in linear algebra, which is essential for data science. The course covers topics such as matrix algebra, determinants, eigenvalues and eigenvectors, diagonalization, and singular value decomposition, which are all used extensively in data analysis and machine learning.

See salaries and explore the career path for Data Scientist

Machine Learning Engineer

Machine Learning Engineers design, develop, and deploy machine learning models to solve real-world problems. The course "Linear Algebra II: Matrices and Linear Transformations" provides a strong foundation in linear algebra, which is essential for machine learning. The course covers topics such as matrix algebra, determinants, eigenvalues and eigenvectors, diagonalization, and singular value decomposition, which are all used extensively in machine learning algorithms.

See salaries and explore the career path for Machine Learning Engineer

Operations Research Analyst

Operations Research Analysts use mathematical and analytical methods to solve complex problems in business and industry. The course "Linear Algebra II: Matrices and Linear Transformations" provides a strong foundation in linear algebra, which is essential for operations research. The course covers topics such as matrix algebra, determinants, eigenvalues and eigenvectors, diagonalization, and singular value decomposition, which are all used extensively in optimization and decision-making.

See salaries and explore the career path for Operations Research Analyst

Actuary

Actuaries use mathematical and statistical methods to assess risk and uncertainty. The course "Linear Algebra II: Matrices and Linear Transformations" provides a strong foundation in linear algebra, which is essential for actuarial science. The course covers topics such as matrix algebra, determinants, eigenvalues and eigenvectors, diagonalization, and singular value decomposition, which are all used extensively in insurance and risk management.

See salaries and explore the career path for Actuary

Financial Analyst

Financial Analysts use financial data and analysis to make investment recommendations. The course "Linear Algebra II: Matrices and Linear Transformations" provides a strong foundation in linear algebra, which is essential for financial analysis. The course covers topics such as matrix algebra, determinants, eigenvalues and eigenvectors, diagonalization, and singular value decomposition, which are all used extensively in portfolio management and investment analysis.

See salaries and explore the career path for Financial Analyst

Software Engineer

Software Engineers design, develop, and maintain software systems. The course "Linear Algebra II: Matrices and Linear Transformations" may be useful for Software Engineers who work on graphics, computer vision, or machine learning applications. The course covers topics such as matrix algebra, determinants, eigenvalues and eigenvectors, diagonalization, and singular value decomposition, which are all used extensively in these areas.

See salaries and explore the career path for Software Engineer

Control Systems Engineer

Control Systems Engineers design and implement systems that control physical processes. The course "Linear Algebra II: Matrices and Linear Transformations" may be useful for Control Systems Engineers who work on complex control systems. The course covers topics such as matrix algebra, determinants, eigenvalues and eigenvectors, diagonalization, and singular value decomposition, which are all used extensively in control theory.

See salaries and explore the career path for Control Systems Engineer

Statistician

Statisticians collect, analyze, and interpret data. The course "Linear Algebra II: Matrices and Linear Transformations" may be useful for Statisticians who work on multivariate data analysis. The course covers topics such as matrix algebra, determinants, eigenvalues and eigenvectors, diagonalization, and singular value decomposition, which are all used extensively in multivariate statistics.

See salaries and explore the career path for Statistician

Economist

Economists study the production, distribution, and consumption of goods and services. The course "Linear Algebra II: Matrices and Linear Transformations" may be useful for Economists who work on econometrics. The course covers topics such as matrix algebra, determinants, eigenvalues and eigenvectors, diagonalization, and singular value decomposition, which are all used extensively in econometrics.

See salaries and explore the career path for Economist

Market Researcher

Market Researchers study consumer behavior and trends. The course "Linear Algebra II: Matrices and Linear Transformations" may be useful for Market Researchers who work on multivariate data analysis. The course covers topics such as matrix algebra, determinants, eigenvalues and eigenvectors, diagonalization, and singular value decomposition, which are all used extensively in multivariate statistics.

See salaries and explore the career path for Market Researcher

Geophysicist

Geophysicists study the physical properties of the Earth. The course "Linear Algebra II: Matrices and Linear Transformations" may be useful for Geophysicists who work on seismic data analysis. The course covers topics such as matrix algebra, determinants, eigenvalues and eigenvectors, diagonalization, and singular value decomposition, which are all used extensively in seismic data analysis.

See salaries and explore the career path for Geophysicist

Aerospace Engineer

Aerospace Engineers design, develop, and test aircraft, spacecraft, and other aerospace vehicles. The course "Linear Algebra II: Matrices and Linear Transformations" may be useful for Aerospace Engineers who work on flight dynamics and control. The course covers topics such as matrix algebra, determinants, eigenvalues and eigenvectors, diagonalization, and singular value decomposition, which are all used extensively in flight dynamics and control.

See salaries and explore the career path for Aerospace Engineer

Mechanical Engineer

Mechanical Engineers design, develop, and test mechanical systems. The course "Linear Algebra II: Matrices and Linear Transformations" may be useful for Mechanical Engineers who work on robotics and control systems. The course covers topics such as matrix algebra, determinants, eigenvalues and eigenvectors, diagonalization, and singular value decomposition, which are all used extensively in robotics and control systems.

See salaries and explore the career path for Mechanical Engineer

Civil Engineer

Civil Engineers design, build, and maintain infrastructure projects such as roads, bridges, and buildings. The course "Linear Algebra II: Matrices and Linear Transformations" may be useful for Civil Engineers who work on structural analysis and design. The course covers topics such as matrix algebra, determinants, eigenvalues and eigenvectors, diagonalization, and singular value decomposition, which are all used extensively in structural analysis and design.

See salaries and explore the career path for Civil Engineer