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Greg Mayer
Your ability to apply the concepts that we introduced in our previous course is enhanced when you can perform algebraic operations with matrices. At the start of this class, you will see how we can apply the Invertible Matrix Theorem to describe how a square matrix might be used to solve linear equations. This theorem is a fundamental role in linear algebra, as it synthesizes many of the concepts introduced in the first course into one succinct concept.
Read more
Your ability to apply the concepts that we introduced in our previous course is enhanced when you can perform algebraic operations with matrices. At the start of this class, you will see how we can apply the Invertible Matrix Theorem to describe how a square matrix might be used to solve linear equations. This theorem is a fundamental role in linear algebra, as it synthesizes many of the concepts introduced in the first course into one succinct concept.
Read more
Your ability to apply the concepts that we introduced in our previous course is enhanced when you can perform algebraic operations with matrices. At the start of this class, you will see how we can apply the Invertible Matrix Theorem to describe how a square matrix might be used to solve linear equations. This theorem is a fundamental role in linear algebra, as it synthesizes many of the concepts introduced in the first course into one succinct concept.
You will then explore theorems and algorithms that will allow you to apply linear algebra in ways that involve two or more matrices. You will examine partitioned matrices and matrix factorizations, which appear in most modern uses of linear algebra. You will also explore two applications of matrix algebra, to economics and to computer graphics.
Students taking this class are encouraged to first complete the first course in this series, linear equations.
What you'll learn
Upon completion of this course, learners will be able to:
- Apply matrix algebra, the matrix transpose, and the zero and identity matrices, to solve and analyze matrix equations.
- Apply the formal definition of an inverse, and its algebraic properties, to solve and analyze linear systems.
- Characterize the invertibility of a matrix using the Invertible Matrix Theorem.
- Apply partitioned matrices to solve problems regarding matrix invertibility and matrix multiplication.
- Compute an LU factorization of a matrix and apply the LU factorization to solve systems of equations.
- Apply matrix algebra and inverses to solve and analyze Leontif Input-Output problems.
- Construct transformation matrices to represent composite transforms in 2D and 3D using homogeneous coordinates.
- Construct a basis for a subspace.
- Calculate the coordinates of a vector in a given basis.
- Characterize a matrix using the concepts of rank, column space, and null space.
- Apply the Rank, Basis, and Matrix Invertibility theorems to describe matrices, subspaces, and systems.
Register for this course and see more details by visiting:
OpenCourser.com/course/7yzw9j/linear
What's inside
Learning objectives
- Apply matrix algebra, the matrix transpose, and the zero and identity matrices, to solve and analyze matrix equations.
- Apply the formal definition of an inverse, and its algebraic properties, to solve and analyze linear systems.
- Characterize the invertibility of a matrix using the invertible matrix theorem.
- Apply partitioned matrices to solve problems regarding matrix invertibility and matrix multiplication.
- Compute an lu factorization of a matrix and apply the lu factorization to solve systems of equations.
- Apply matrix algebra and inverses to solve and analyze leontif input-output problems.
- Construct transformation matrices to represent composite transforms in 2d and 3d using homogeneous coordinates.
- Construct a basis for a subspace.
- Calculate the coordinates of a vector in a given basis.
- Characterize a matrix using the concepts of rank, column space, and null space.
- Apply the rank, basis, and matrix invertibility theorems to describe matrices, subspaces, and systems.
- Apply matrix algebra, the matrix transpose, and the zero and identity matrices, to solve and analyze matrix equations.
- Apply the formal definition of an inverse, and its algebraic properties, to solve and analyze linear systems.
- Characterize the invertibility of a matrix using the invertible matrix theorem.
- Apply partitioned matrices to solve problems regarding matrix invertibility and matrix multiplication.
- Compute an lu factorization of a matrix and apply the lu factorization to solve systems of equations.
- Apply matrix algebra and inverses to solve and analyze leontif input-output problems.
- Construct transformation matrices to represent composite transforms in 2d and 3d using homogeneous coordinates.
- Construct a basis for a subspace.
- Calculate the coordinates of a vector in a given basis.
- Characterize a matrix using the concepts of rank, column space, and null space.
- Apply the rank, basis, and matrix invertibility theorems to describe matrices, subspaces, and systems.
Good to know
Good to know
Know what's good ,
what to watch for , and
possible dealbreakers
Explores theorems and algorithms that apply linear algebra in ways involving two or more matrices
Taught by Greg Mayer, who is recognized for their work in linear algebra
Develops key skills in matrix algebra and inverses, which are core skills for advanced mathematics and computer science
Recommended for students with prior experience in linear equations
Covers the Invertible Matrix Theorem, a fundamental concept in linear algebra
Builds a strong foundation for intermediate learners in linear algebra
Save this course
Save Linear Algebra II: Matrix Algebra to your list so you can find it easily later:
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Activities
Be better prepared
before
your course. Deepen your understanding
during
and
after
it. Supplement your coursework and achieve mastery of the topics covered
in Linear Algebra II: Matrix Algebra with these
activities:
Review Matrices and Matrix Operations
Show steps
Review basic concepts like matrix addition, subtraction, scalar multiplication, and matrix multiplication to strengthen your foundation for more advanced topics.
Browse courses on
Matrices
Show steps
-
Recall basic matrix properties and definitions.
-
Practice performing basic matrix operations on small examples.
-
Solve simple linear equations using matrix operations.
Participate in a Study Group for Matrix Algebra
Show steps
Engage in collaborative learning by joining a study group with peers. Discuss concepts, solve problems together, and reinforce your understanding through peer-to-peer interactions.
Browse courses on
Matrix Algebra
Show steps
-
Join or form a study group with other students taking the course.
-
Schedule regular meetings to discuss course material, solve problems, and quiz each other.
Explore MIT OpenCourseWare Lectures on Matrix Algebra
Show steps
Gain additional insights and perspectives by watching video lectures from MIT OpenCourseWare. These lectures provide clear and engaging explanations of matrix algebra concepts.
Browse courses on
Matrix Algebra
Show steps
-
Watch lectures on topics relevant to the course, such as matrix operations, inverses, and systems of equations.
-
Take notes and pause the videos to reflect on the concepts.
Four other activities
Expand to see all activities and additional details
Show all seven activities
Solve Matrix Equations Involving Inverses
Show steps
Strengthen your understanding of matrix inverses and their applications by solving various matrix equations involving inverses.
Show steps
-
Review the concept of matrix inverses and their properties.
-
Practice finding inverses of matrices using various methods.
-
Solve matrix equations by applying matrix inverses.
Create Visual Aids for Matrix Concepts
Show steps
Enhance your comprehension by creating visual aids such as diagrams, charts, or mind maps that represent matrix concepts. This will help you visualize and understand the relationships between matrix elements.
Browse courses on
Visual Aids
Show steps
-
Identify key matrix concepts that you want to represent visually.
-
Choose appropriate visual formats, such as diagrams, charts, or mind maps.
-
Create visual aids that clearly illustrate the concepts and their relationships.
Read 'Linear Algebra and Its Applications' by Gilbert Strang
Show steps
Delve deeper into the concepts covered in the course by reading this classic textbook. It provides comprehensive explanations and insightful examples that will enhance your understanding and retention.
View
Linear Algebra for Everyone
on Amazon
Show steps
-
Read the relevant chapters covering matrix algebra and linear systems.
-
Work through the practice problems and exercises provided in the book.
Develop a Matrix Algebra Toolkit
Show steps
Create a collection of custom functions or a software tool that automates matrix operations and solves matrix equations. This will provide you with a valuable resource for future work involving matrix algebra.
Browse courses on
Custom Functions
Show steps
-
Identify the specific matrix operations and equations that you want to automate.
-
Design and develop custom functions or a software tool that implements these operations and equations.
-
Test and refine your tool to ensure accuracy and efficiency.
Review Matrices and Matrix Operations
Show steps
Review basic concepts like matrix addition, subtraction, scalar multiplication, and matrix multiplication to strengthen your foundation for more advanced topics.
Browse courses on
Matrices
Show steps
Show steps
Show steps
- Recall basic matrix properties and definitions.
- Practice performing basic matrix operations on small examples.
- Solve simple linear equations using matrix operations.
Participate in a Study Group for Matrix Algebra
Show steps
Engage in collaborative learning by joining a study group with peers. Discuss concepts, solve problems together, and reinforce your understanding through peer-to-peer interactions.
Browse courses on
Matrix Algebra
Show steps
Show steps
Show steps
- Join or form a study group with other students taking the course.
- Schedule regular meetings to discuss course material, solve problems, and quiz each other.
Explore MIT OpenCourseWare Lectures on Matrix Algebra
Show steps
Gain additional insights and perspectives by watching video lectures from MIT OpenCourseWare. These lectures provide clear and engaging explanations of matrix algebra concepts.
Browse courses on
Matrix Algebra
Show steps
Show steps
Show steps
- Watch lectures on topics relevant to the course, such as matrix operations, inverses, and systems of equations.
- Take notes and pause the videos to reflect on the concepts.
Four other activities
Expand to see all activities and additional details
Show all seven activities
Solve Matrix Equations Involving Inverses
Show steps
Strengthen your understanding of matrix inverses and their applications by solving various matrix equations involving inverses.
Show steps
Show steps
Show steps
- Review the concept of matrix inverses and their properties.
- Practice finding inverses of matrices using various methods.
- Solve matrix equations by applying matrix inverses.
Create Visual Aids for Matrix Concepts
Show steps
Enhance your comprehension by creating visual aids such as diagrams, charts, or mind maps that represent matrix concepts. This will help you visualize and understand the relationships between matrix elements.
Browse courses on
Visual Aids
Show steps
Show steps
Show steps
- Identify key matrix concepts that you want to represent visually.
- Choose appropriate visual formats, such as diagrams, charts, or mind maps.
- Create visual aids that clearly illustrate the concepts and their relationships.
Read 'Linear Algebra and Its Applications' by Gilbert Strang
Show steps
Delve deeper into the concepts covered in the course by reading this classic textbook. It provides comprehensive explanations and insightful examples that will enhance your understanding and retention.
View
Linear Algebra for Everyone
on Amazon
Show steps
Show steps
Show steps
- Read the relevant chapters covering matrix algebra and linear systems.
- Work through the practice problems and exercises provided in the book.
Develop a Matrix Algebra Toolkit
Show steps
Create a collection of custom functions or a software tool that automates matrix operations and solves matrix equations. This will provide you with a valuable resource for future work involving matrix algebra.
Browse courses on
Custom Functions
Show steps
Show steps
Show steps
- Identify the specific matrix operations and equations that you want to automate.
- Design and develop custom functions or a software tool that implements these operations and equations.
- Test and refine your tool to ensure accuracy and efficiency.
Career center
Learners who complete Linear Algebra II: Matrix Algebra will develop knowledge and skills
that may be useful to these careers:
Quantitative Analyst
Quantitative Analyst
Quantitative Analysts use their knowledge of mathematics and computer science to analyze data and identify trends. In this role, you will use matrix algebra and other mathematical concepts to develop and implement quantitative models. This course will introduce you to the fundamental concepts of matrix algebra, which will be essential for you to understand the quantitative models that you will use on a daily basis. Linear Algebra II: Matrix Algebra can help you to succeed as a Quantitative Analyst by providing you with the mathematical foundation you need to excel in this role.
Data Scientist
Data Scientist
Data Scientists use their knowledge of mathematics, statistics, and computer science to analyze data and extract insights. In this role, you will use matrix algebra and other mathematical concepts to develop data mining algorithms and models. This course will help you to develop the mathematical skills you need to become a successful Data Scientist. Linear Algebra II: Matrix Algebra will provide you with the mathematical foundation you need to excel in this role.
Operations Research Analyst
Operations Research Analyst
Operations Research Analysts use their knowledge of mathematics and computer science to solve business problems. In this role, you will use matrix algebra and other mathematical concepts to develop and implement optimization models. This course will introduce you to the fundamental concepts of matrix algebra, which will be essential for you to understand the optimization models that you will use on a daily basis. Linear Algebra II: Matrix Algebra will help you to develop the mathematical skills you need to become a successful Operations Research Analyst.
Computer Programmer
Computer Programmer
Computer Programmers use their knowledge of computer science to develop and implement software applications. In this role, you will use matrix algebra and other mathematical concepts to develop algorithms and data structures. This course will introduce you to the fundamental concepts of matrix algebra, which will be essential for you to understand the algorithms and data structures that you will use on a daily basis. Linear Algebra II: Matrix Algebra will help you to develop the mathematical skills you need to become a successful Computer Programmer.
Financial Analyst
Financial Analyst
Financial Analysts use their knowledge of mathematics and economics to analyze financial data and make investment recommendations. In this role, you will use matrix algebra and other mathematical concepts to develop financial models. This course will introduce you to the fundamental concepts of matrix algebra, which will be essential for you to understand the financial models that you will use on a daily basis. Linear Algebra II: Matrix Algebra will provide you with the mathematical foundation you need to excel in this role.
Actuary
Actuary
Actuaries use their knowledge of mathematics and statistics to assess risk and develop insurance policies. In this role, you will use matrix algebra and other mathematical concepts to develop actuarial models. This course will introduce you to the fundamental concepts of matrix algebra, which will be essential for you to understand the actuarial models that you will use on a daily basis. Linear Algebra II: Matrix Algebra will provide you with the mathematical foundation you need to excel in this role.
Mathematician
Mathematician
Mathematicians use their knowledge of mathematics to solve problems and develop new theories. In this role, you will use matrix algebra and other mathematical concepts to conduct research in various fields of mathematics. This course will introduce you to the fundamental concepts of matrix algebra, which will be essential for you to understand the research that you will conduct on a daily basis. Linear Algebra II: Matrix Algebra will help you to develop the mathematical skills you need to become a successful Mathematician.
Statistician
Statistician
Statisticians use their knowledge of mathematics and statistics to collect and analyze data. In this role, you will use matrix algebra and other mathematical concepts to develop statistical models. This course will introduce you to the fundamental concepts of matrix algebra, which will be essential for you to understand the statistical models that you will use on a daily basis. Linear Algebra II: Matrix Algebra will help you to develop the mathematical skills you need to become a successful Statistician.
Data Analyst
Data Analyst
Data Analysts use their knowledge of mathematics and computer science to analyze data and extract insights. In this role, you will use matrix algebra and other mathematical concepts to develop data mining algorithms and models. This course will introduce you to the fundamental concepts of matrix algebra, which will be essential for you to understand the data mining algorithms and models that you will use on a daily basis. Linear Algebra II: Matrix Algebra is a key course for anyone who wants to enter the field of Data Analytics. It will provide you with the mathematical foundation you need to excel in this role.
Software Engineer
Software Engineer
Software Engineers use their knowledge of computer science to design and develop software applications. In this role, you will use matrix algebra and other mathematical concepts to develop algorithms and data structures. This course will introduce you to the fundamental concepts of matrix algebra, which will be essential for you to understand the algorithms and data structures that you will use on a daily basis. Linear Algebra II: Matrix Algebra is a key course for anyone who wants to enter the field of Software Engineering. It will provide you with the mathematical foundation you need to excel in this role.
Computer Scientist
Computer Scientist
Computer Scientists use their knowledge of computer science to design and develop software applications. In this role, you will use matrix algebra and other mathematical concepts to develop algorithms and data structures. This course will introduce you to the fundamental concepts of matrix algebra, which will be essential for you to understand the algorithms and data structures that you will use on a daily basis. Linear Algebra II: Matrix Algebra is a key course for anyone who wants to enter the field of Computer Science. It will provide you with the mathematical foundation you need to excel in this role.
Financial Manager
Financial Manager
Financial Managers use their knowledge of finance to manage the financial resources of a company or organization. In this role, you will use matrix algebra and other mathematical concepts to develop financial models. This course will introduce you to the fundamental concepts of matrix algebra, which will be essential for you to understand the financial models that you will use on a daily basis. Linear Algebra II: Matrix Algebra is a key course for anyone who wants to enter the field of Financial Management. It will provide you with the mathematical foundation you need to excel in this role.
Economist
Economist
Economists use their knowledge of economics to analyze economic data and develop economic models. In this role, you will use matrix algebra and other mathematical concepts to develop economic models. This course will introduce you to the fundamental concepts of matrix algebra, which will be essential for you to understand the economic models that you will use on a daily basis. Linear Algebra II: Matrix Algebra is a key course for anyone who wants to enter the field of Economics. It will provide you with the mathematical foundation you need to excel in this role.
Operations Manager
Operations Manager
Operations Managers use their knowledge of operations management to manage the operations of a company or organization. In this role, you will use matrix algebra and other mathematical concepts to develop operations management models. This course will introduce you to the fundamental concepts of matrix algebra, which will be essential for you to understand the operations management models that you will use on a daily basis. Linear Algebra II: Matrix Algebra is a key course for anyone who wants to enter the field of Operations Management. It will provide you with the mathematical foundation you need to excel in this role.
Market Researcher
Market Researcher
Market Researchers use their knowledge of marketing and research to conduct market research studies. In this role, you will use matrix algebra and other mathematical concepts to analyze market research data. This course will introduce you to the fundamental concepts of matrix algebra, which will be essential for you to understand the market research data that you will use on a daily basis. Linear Algebra II: Matrix Algebra is a key course for anyone who wants to enter the field of Market Research. It will provide you with the mathematical foundation you need to excel in this role.
For more career information including salaries, visit:
OpenCourser.com/course/7yzw9j/linear
Reading list
We've selected 14 books
that we think will supplement your
learning. Use these to
develop background knowledge, enrich your coursework, and gain a
deeper understanding of the topics covered in
Linear Algebra II: Matrix Algebra.
Provides a comprehensive overview of linear algebra, covering topics such as matrix algebra, systems of linear equations, vector spaces, and eigenvalues and eigenvectors. It classic textbook that is widely used in undergraduate linear algebra courses.
Provides a more advanced treatment of linear algebra. It covers topics such as abstract vector spaces, linear transformations, and inner product spaces. It good choice for students who have a strong background in mathematics.
Save
Provides a comprehensive treatment of matrix analysis. It covers topics such as matrix norms, eigenvalues and eigenvectors, and singular value decomposition. It good choice for students who are interested in learning more about the theory of matrices.
Provides an introduction to numerical linear algebra. It covers topics such as matrix computations, eigenvalue algorithms, and iterative methods. It good choice for students who are interested in learning more about the numerical aspects of linear algebra.
Provides a modern introduction to linear algebra. It covers topics such as vector spaces, linear transformations, and matrices. It good choice for students who are looking for a clear and concise introduction to linear algebra.
Provides a comprehensive treatment of linear algebra. It covers topics such as matrix algebra, systems of linear equations, vector spaces, and eigenvalues and eigenvectors. It good choice for students who are looking for a rigorous treatment of linear algebra.
Provides an introduction to applied linear algebra. It covers topics such as matrix algebra, systems of linear equations, and vector spaces. It good choice for students who are interested in learning how linear algebra is used in applications.
Provides an introduction to linear algebra with a focus on applications in R. It covers topics such as matrix algebra, systems of linear equations, and vector spaces. It good choice for students who are interested in learning how linear algebra is used in R.
Save
Provides a step-by-step introduction to linear algebra. It covers topics such as matrix algebra, systems of linear equations, and vector spaces. It good choice for students who are new to linear algebra and want to learn at their own pace.
Provides a comprehensive review of linear algebra. It covers topics such as matrix algebra, systems of linear equations, and vector spaces. It good choice for students who are preparing for exams or who want to brush up on their linear algebra skills.
Provides an introduction to the mathematics that is used in machine learning. It covers topics such as linear algebra, calculus, and probability. It good choice for students who are interested in learning more about the mathematical foundations of machine learning.
Save
Provides an introduction to deep learning. It covers topics such as neural networks, convolutional neural networks, and recurrent neural networks. It good choice for students who are interested in learning more about the theory and practice of deep learning.
Provides a comprehensive overview of artificial intelligence. It covers topics such as search, planning, machine learning, and natural language processing. It good choice for students who are interested in learning more about the theory and practice of artificial intelligence.
Provides a comprehensive overview of statistical learning. It covers topics such as supervised learning, unsupervised learning, and reinforcement learning. It good choice for students who are interested in learning more about the theory and practice of statistical learning.
For more information about how these books relate to this course, visit:
OpenCourser.com/course/7yzw9j/linear
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Effort
5 to 6 hours per week for 3 weeks
Level
Introductory
Via
edX
Institution
The Georgia Institute of Technology
Instructor
Greg Mayer
Sessions
August 17, 2026
- January 1, 2027
May 11, 2026
- August 9, 2026
January 5, 2026
- May 10, 2026
August 18, 2025
- January 1, 2026
May 12, 2025
- August 10, 2025
January 6, 2025
- May 10, 2025
August 19, 2024
- January 1, 2025
May 13, 2024
- August 11, 2024
January 8, 2024
- May 12, 2024
Language
English
Transcript
English
This course belongs to a
collection
called
Introductory Linear Algebra. It's comprised of two courses:
- Linear Algebra I: Linear Equations
- Linear Algebra II: Matrix Algebra (viewing)
Good to know
Explores theorems and algorithms that apply linear algebra in ways involving two or more matrices
Taught by Greg Mayer, who is recognized for their work in linear algebra
Develops key skills in matrix algebra and inverses, which are core skills for advanced mathematics and computer science
Recommended for students with prior experience in linear equations
Covers the Invertible Matrix Theorem, a fundamental concept in linear algebra
Builds a strong foundation for intermediate learners in linear algebra
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