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Daniel Boley
Mathematical Matrix Methods lie at the root of most methods of machine learning and data analysis of tabular data. Learn the basics of Matrix Methods, including matrix-matrix multiplication, solving linear equations, orthogonality, and best least squares approximation. Discover the Singular Value Decomposition that plays a fundamental role in dimensionality reduction, Principal Component Analysis, and noise reduction. Optional examples using Python are used to illustrate the concepts and allow the learner to experiment with the algorithms.
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What's inside
Syllabus
Matrices as Mathematical Objects
Matrix Multiplication and other Operations
Systems of Linear Equations
Read more
Syllabus
Matrices as Mathematical Objects
Matrix Multiplication and other Operations
Systems of Linear Equations
Read more
Linear Least Squares
Singular Value Decomposition
Good to know
Good to know
Know what's good ,
what to watch for , and
possible dealbreakers
Delves into the fundamentals of Mathematical Matrix Methods, making it suitable for learners new to the topic
Provides a strong foundation in matrix theory, which underlies many data analysis techniques
Explores Singular Value Decomposition, a crucial concept in dimensionality reduction and noise reduction
Optional Python examples enhance understanding and allow learners to practice algorithms
Incorporates practical examples to illustrate concepts, aiding in comprehension
Save this course
Save Matrix Methods to your list so you can find it easily later:
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Reviews summary
Well received matrix methods overview
Learners say that Matrix Methods is a largely positive overview of key topics in linear algebra. The course is well received for its engaging assignments and clear explanations in the first three weeks. However, learners note that the difficulty of this course is not introductory and requires some prior experience in linear algebra or matrix algebra. Overall, students recommend this course for those with a background in linear algebra who want to refresh their knowledge or gain a practical understanding of matrix applications.
Introduces complex concepts in digestible parts.
"The first 3 weeks are well structured and introduce complex concepts in digestible parts"
"The course is taught interestingly for the first 3 weeks."
Assignments are challenging and help understanding.
"Really its very informative and basic material provided. I enjoyed and learn a lot"
"Couresa is very helpful of learning skill about matrix .this is very helpful for me"
"Very good course, the questions are really challenging..."
Not much practical Python programming.
"The python content in this course is almost zero. The only thing I learn useful is the section about "singualr value decomposition" (the only reason why I still give it a 2-star review). However there's no lecture about the topic but two papers to read through."
"I found the course very unbalanced and without much effort applied to it.Some parts were easy to understand - the worked examples helped a lot, while others, with less videos and based on links, required a lot of work, namely because of the specific terminology used."
Videos are hit or miss in quality.
"The course topics are interesting, unfortunately a video on week 5 would have been very important.there are several errors in the test which made completing the test unnecessary difficult."
"I did learn some things, so I hate to review the course harshly, but there were numerous errors in the quizzes which have been there for a long time (based on forum comments) and have not been addressed."
Some explanations may need more detail.
"The topics of the course are good, nevertheless, the videos need explain all the topics in detail because, sometimes is hard to understand just reading the pdf materials."
"Fun course, but feels like they don't supply all the necessary information for the latter section of the course. Had to supplement with self found information to complete this course."
Assumes prior knowledge in linear algebra.
"The difficulty of this course is not introductory and there is a hurdle for some of the beginners in linear algebra."
"I wouldn't take this course...I'm happy with the methods covered, and I found the first 2 weeks useful practice. However, it seems like the professor spent about 2 hours making the course."
"The course topics are very important for Data Science and Machine Learning. However, except for a few resource materials in PDF document, the course does not meet the expectations and standards."
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 Matrix Methods with these
activities:
Read 'Matrix Methods' by Daniel Boley
Show steps
This book provides a comprehensive overview of matrix methods. Reading this book will help you solidify your understanding of the concepts covered in this course.
Show steps
-
Purchase a copy of the book.
-
Read the book and take notes.
-
Complete the practice problems.
Follow a tutorial on matrix multiplication
Show steps
Matrix multiplication is a fundamental operation in linear algebra. This activity will help you learn how to perform matrix multiplication and understand its applications.
Browse courses on
Matrix Algebra
Show steps
-
Find a tutorial on matrix multiplication.
-
Follow the tutorial and complete the practice problems.
Solve matrix equations
Show steps
Solving matrix equations is a fundamental skill in linear algebra. This activity will help you practice solving matrix equations and improve your understanding of the concepts involved.
Browse courses on
Matrix Algebra
Show steps
-
Start by reviewing the basics of matrix algebra.
-
Then, practice solving simple matrix equations.
-
Once you have a good understanding of the basics, you can move on to more challenging problems.
Five other activities
Expand to see all activities and additional details
Show all eight activities
Solve systems of linear equations
Show steps
Solving systems of linear equations is a fundamental skill in linear algebra. This activity will help you practice solving systems of linear equations and improve your understanding of the concepts involved.
Browse courses on
Matrix Algebra
Show steps
-
Start by reviewing the basics of solving systems of linear equations.
-
Then, practice solving simple systems of linear equations.
-
Once you have a good understanding of the basics, you can move on to more challenging problems.
Discuss matrix methods with classmates
Show steps
Discussing matrix methods with classmates can help you solidify your understanding of the concepts and learn from others.
Browse courses on
Matrix Algebra
Show steps
-
Find a study partner or group.
-
Meet regularly to discuss the course material.
-
Work together on practice problems.
Attend a workshop on matrix methods
Show steps
Attending a workshop on matrix methods can help you learn from experts and get hands-on experience.
Browse courses on
Matrix Algebra
Show steps
-
Find a workshop that is relevant to your interests.
-
Register for the workshop.
-
Attend the workshop and participate in the activities.
Create a presentation on the Singular Value Decomposition
Show steps
The Singular Value Decomposition (SVD) is a powerful tool for data analysis. This activity will help you learn about the SVD and how to use it to solve real-world problems.
Browse courses on
Singular Value Decomposition
Show steps
-
Start by researching the SVD.
-
Then, develop a presentation on the SVD.
-
Finally, present your findings to the class.
Create a blog post on matrix methods
Show steps
Creating a blog post on matrix methods will help you solidify your understanding of the concepts and share your knowledge with others.
Browse courses on
Matrix Algebra
Show steps
-
Choose a topic for your blog post.
-
Research the topic and write a draft of your post.
-
Edit and publish your post.
Read 'Matrix Methods' by Daniel Boley
Show steps
This book provides a comprehensive overview of matrix methods. Reading this book will help you solidify your understanding of the concepts covered in this course.
Show steps
Show steps
Show steps
- Purchase a copy of the book.
- Read the book and take notes.
- Complete the practice problems.
Follow a tutorial on matrix multiplication
Show steps
Matrix multiplication is a fundamental operation in linear algebra. This activity will help you learn how to perform matrix multiplication and understand its applications.
Browse courses on
Matrix Algebra
Show steps
Show steps
Show steps
- Find a tutorial on matrix multiplication.
- Follow the tutorial and complete the practice problems.
Solve matrix equations
Show steps
Solving matrix equations is a fundamental skill in linear algebra. This activity will help you practice solving matrix equations and improve your understanding of the concepts involved.
Browse courses on
Matrix Algebra
Show steps
Show steps
Show steps
- Start by reviewing the basics of matrix algebra.
- Then, practice solving simple matrix equations.
- Once you have a good understanding of the basics, you can move on to more challenging problems.
Five other activities
Expand to see all activities and additional details
Show all eight activities
Solve systems of linear equations
Show steps
Solving systems of linear equations is a fundamental skill in linear algebra. This activity will help you practice solving systems of linear equations and improve your understanding of the concepts involved.
Browse courses on
Matrix Algebra
Show steps
Show steps
Show steps
- Start by reviewing the basics of solving systems of linear equations.
- Then, practice solving simple systems of linear equations.
- Once you have a good understanding of the basics, you can move on to more challenging problems.
Discuss matrix methods with classmates
Show steps
Discussing matrix methods with classmates can help you solidify your understanding of the concepts and learn from others.
Browse courses on
Matrix Algebra
Show steps
Show steps
Show steps
- Find a study partner or group.
- Meet regularly to discuss the course material.
- Work together on practice problems.
Attend a workshop on matrix methods
Show steps
Attending a workshop on matrix methods can help you learn from experts and get hands-on experience.
Browse courses on
Matrix Algebra
Show steps
Show steps
Show steps
- Find a workshop that is relevant to your interests.
- Register for the workshop.
- Attend the workshop and participate in the activities.
Create a presentation on the Singular Value Decomposition
Show steps
The Singular Value Decomposition (SVD) is a powerful tool for data analysis. This activity will help you learn about the SVD and how to use it to solve real-world problems.
Browse courses on
Singular Value Decomposition
Show steps
Show steps
Show steps
- Start by researching the SVD.
- Then, develop a presentation on the SVD.
- Finally, present your findings to the class.
Create a blog post on matrix methods
Show steps
Creating a blog post on matrix methods will help you solidify your understanding of the concepts and share your knowledge with others.
Browse courses on
Matrix Algebra
Show steps
Show steps
Show steps
- Choose a topic for your blog post.
- Research the topic and write a draft of your post.
- Edit and publish your post.
Career center
Learners who complete Matrix Methods will develop knowledge and skills
that may be useful to these careers:
Machine Learning Engineer
Machine Learning Engineer
Machine Learning Engineers design, develop, and deploy machine learning models to solve real-world problems. Matrix Methods is a highly relevant course for Machine Learning Engineers, as it covers the mathematical foundations of machine learning. By understanding these concepts, learners can build and optimize machine learning models more effectively.
Data Scientist
Data Scientist
Data Scientists use their expertise in mathematics, statistics, and machine learning to extract valuable insights from large datasets. The Matrix Methods course can provide a solid foundation for aspiring Data Scientists, as it covers the fundamentals of matrix operations, linear equations, and the Singular Value Decomposition (SVD). These concepts are essential for understanding and applying advanced machine learning algorithms used in data science.
Data Analyst
Data Analyst
Data Analysts use statistical and machine learning techniques to analyze data and extract insights. Matrix Methods is a valuable course for Data Analysts, as it provides a strong foundation in the mathematical principles used in data analysis. By understanding these concepts, learners can perform data analysis more effectively and communicate their findings more clearly.
Quantitative Analyst
Quantitative Analyst
Quantitative Analysts use mathematical and statistical models to analyze financial data and make investment decisions. The Matrix Methods course can be beneficial for Quantitative Analysts, as it covers the mathematical techniques used in financial modeling and risk management. By understanding these concepts, learners can develop more sophisticated models and make more informed investment decisions.
Statistician
Statistician
Statisticians collect, analyze, and interpret data to draw conclusions about the world around us. The Matrix Methods course can be useful for Statisticians, as it covers the mathematical techniques used in statistical analysis. By understanding these concepts, learners can perform statistical analysis more effectively and communicate their findings more clearly.
Financial Analyst
Financial Analyst
Financial Analysts analyze financial data to make investment recommendations to clients. Matrix Methods is a helpful course for Financial Analysts, as it provides a foundation in the mathematical techniques used in financial modeling and analysis. By understanding these concepts, learners can develop more accurate financial models and make more informed investment recommendations.
Operations Research Analyst
Operations Research Analyst
Operations Research Analysts use mathematical and analytical techniques to solve complex problems in business and industry. The Matrix Methods course can be useful for Operations Research Analysts, as it covers the mathematical techniques used in optimization and modeling. By understanding these concepts, learners can develop more effective solutions to business problems.
Actuary
Actuary
Actuaries use mathematical and statistical techniques to assess risk and uncertainty in the insurance and finance industries. The Matrix Methods course can be helpful for Actuaries, as it covers the mathematical techniques used in risk assessment and modeling. By understanding these concepts, learners can develop more accurate risk models and make more informed decisions.
Applied Mathematician
Applied Mathematician
Applied Mathematicians use mathematical techniques to solve problems in science, engineering, and business. Matrix Methods is a helpful course for Applied Mathematicians who work in data analysis or machine learning.
Computer Scientist
Computer Scientist
Computer Scientists research and develop new computing technologies. Matrix Methods is a helpful course for Computer Scientists who work on machine learning or data analysis.
Biostatistician
Biostatistician
Biostatisticians use statistical methods to analyze biological data. Matrix Methods is a helpful course for Biostatisticians who work with high-dimensional data.
Software Engineer
Software Engineer
Software Engineers design, develop, and maintain software systems. Matrix Methods is a helpful course for Software Engineers who work on data-intensive applications.
Economist
Economist
Economists use mathematical and statistical techniques to analyze economic data and make predictions about the economy. The Matrix Methods course can be helpful for Economists, as it covers the mathematical techniques used in economic modeling and analysis.
Epidemiologist
Epidemiologist
Epidemiologists study the causes and patterns of disease. Matrix Methods is a helpful course for Epidemiologists who work with large datasets.
Psychometrician
Psychometrician
Psychometricians use statistical methods to measure psychological traits and abilities. Matrix Methods is a helpful course for Psychometricians who work with large datasets.
For more career information including salaries, visit:
OpenCourser.com/course/gc4ho0/matrix
Reading list
We've selected 12 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
Matrix Methods.
Provides a comprehensive introduction to linear algebra, covering the basics of matrix operations, linear equations, and vector spaces. It valuable reference for students who want to deepen their understanding of the mathematical concepts behind matrix methods.
Provides a more advanced treatment of matrix methods, covering topics such as eigenvalues, eigenvectors, and matrix decompositions. It useful reference for students who want to learn more about the theoretical underpinnings of matrix methods.
Save
Provides a comprehensive treatment of matrix computations, covering topics such as matrix factorizations, eigenvalue computations, and singular value decompositions. It valuable reference for students who want to learn more about the numerical aspects of matrix methods.
Provides an introduction to numerical linear algebra, covering topics such as matrix computations, linear equations, and eigenvalue problems. It valuable resource for students who want to learn how to use matrix methods to solve real-world problems.
Provides an introduction to matrix methods in statistics, covering topics such as principal component analysis, factor analysis, and discriminant analysis. It valuable resource for students who want to learn how to use matrix methods to analyze statistical data.
Provides an introduction to matrix methods in econometrics, covering topics such as matrix algebra, linear models, and time series analysis. It valuable resource for students who want to learn how to use matrix methods to analyze economic data.
Provides an introduction to matrix methods for quantum mechanics, covering topics such as matrix algebra, quantum operators, and wave functions. It valuable resource for students who want to learn how to use matrix methods to analyze quantum systems.
Save
Provides an introduction to matrix methods in engineering, covering topics such as matrix algebra, linear equations, and eigenvalues. It valuable resource for students who want to learn how to use matrix methods to solve engineering problems.
Provides a modern and rigorous treatment of linear algebra, covering topics such as vector spaces, linear transformations, and matrices. It valuable reference for students who want to learn more about the theoretical foundations of linear algebra.
Provides an introduction to matrix methods for structural analysis, covering topics such as matrix algebra, force analysis, and displacement analysis. It valuable resource for students who want to learn how to use matrix methods to analyze structural systems.
Save
Provides a comprehensive treatment of matrix analysis, covering topics such as matrix norms, matrix functions, and matrix inequalities. It valuable reference for students who want to learn more about the advanced mathematical theory of matrices.
Provides a comprehensive treatment of matrix theory, covering topics such as matrix norms, matrix functions, and matrix equations. It valuable reference for students who want to learn more about the advanced mathematical theory of matrices.
For more information about how these books relate to this course, visit:
OpenCourser.com/course/gc4ho0/matrix
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University of Minnesota
Instructor
Daniel Boley
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Good to know
Delves into the fundamentals of Mathematical Matrix Methods, making it suitable for learners new to the topic
Provides a strong foundation in matrix theory, which underlies many data analysis techniques
Explores Singular Value Decomposition, a crucial concept in dimensionality reduction and noise reduction
Optional Python examples enhance understanding and allow learners to practice algorithms
Incorporates practical examples to illustrate concepts, aiding in comprehension
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