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Linear Algebra Basics

Dr. S. K. Gupta

Machine learning and data science are the most popular topics of research nowadays. They are applied in all the areas of engineering and sciences. Various machine learning tools provide a data-driven solution to various real-life problems. Basic knowledge of linear algebra is necessary to develop new algorithms for machine learning and data science. In this course, you will learn about the mathematical concepts related to linear algebra, which include vector spaces, subspaces, linear span, basis, and dimension. It also covers linear transformation, rank and nullity of a linear transformation, eigenvalues, eigenvectors, and diagonalization of matrices. The concepts of singular value decomposition, inner product space, and norm of vectors and matrices further enrich the course contents.

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What's inside

Syllabus

Getting Started with the Course
This module provides an overview of the course content and structure. In this module, you will learn about the different course elements. In this module, you will get acquainted with your instructor and get an opportunity to introduce yourself and interact with your peers.
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Traffic lights

Read about what's good
what should give you pause
and possible dealbreakers
Taught by Dr. S. K. Gupta, who is recognized for their work in the field of machine learning and data science
Builds a strong foundation for beginners in linear algebra, which is a core skill for machine learning and data science
Covers the mathematical concepts related to linear algebra, which include vector spaces, subspaces, linear span, basis, and dimension

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Reviews summary

Foundational linear algebra for ml/ds

According to students, this course provides a solid foundational understanding of linear algebra, essential for those entering machine learning and data science. Learners find the content comprehensively covers key concepts like vector spaces, linear transformations, and eigenvalues. The course is seen as a strong theoretical primer, though some might desire more hands-on application. The structured modules are generally appreciated for their clear progression, building up to advanced topics like Singular Value Decomposition. Overall, it serves as a valuable starting point for complex mathematical concepts.
Emphasizes mathematical rigor and proofs, typical of academic institutions.
"I found the mathematical explanations incredibly detailed and precise."
"This course provides a robust theoretical foundation, which I appreciate for deeper understanding."
"It's great for building a solid academic understanding of the principles."
Directly connects linear algebra to machine learning and data science needs.
"I found this course directly applicable to understanding ML algorithms."
"It highlights how linear algebra underpins data science techniques."
"This course made me see the importance of these concepts in real-world ML problems."
A strong base in essential linear algebra concepts.
"I appreciate the thorough coverage of vector spaces and linear transformations."
"The course really helped me grasp the basics needed for my ML studies."
"This course covers all the necessary foundational concepts from vector spaces to SVD."
May be challenging for learners without prior mathematical background.
"I recommend brushing up on basic calculus before diving in, as the pace can be quick."
"Some sections felt a bit rushed, especially if you're new to proofs."
"I had to supplement with external resources to keep up with certain derivations."
Course may benefit from more practical examples or coding exercises.
"I wish there were more coding examples illustrating the concepts in Python or R."
"The theory is strong, but I wanted more practical applications to solidify understanding."
"I found myself seeking external resources for hands-on exercises related to ML."

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 Basics with these activities:
Review Basic Linear Algebra Concepts
Refreshing basic linear algebra concepts can provide a foundation for understanding more advanced topics covered in the course.
Browse courses on Linear Algebra
Show steps
  • Review notes or textbooks on basic linear algebra
  • Solve practice problems to reinforce understanding
Review Matrix Operations
Reviewing matrix operations can provide a foundation for understanding linear transformations and linear equations covered in the course.
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Show steps
  • Identify different matrix operations, such as addition, subtraction, scalar multiplication, and matrix multiplication
  • Practice applying these operations to manipulate matrices
Join a Study Group for Linear Algebra Concepts
Participating in a study group allows for collaborative learning, discussion of concepts, and support from peers, which can enhance understanding throughout the course.
Browse courses on Linear Algebra
Show steps
  • Find or create a study group with classmates
  • Meet regularly to discuss course material
  • Work together on practice problems and assignments
Five other activities
Expand to see all activities and additional details
Show all eight activities
Explore Tutorials on Eigenvalues and Eigenvectors
Tutorials on eigenvalues and eigenvectors can provide additional insights and examples to enhance comprehension of this topic covered in Module 3.
Browse courses on Eigenvalues
Show steps
  • Search for tutorials on eigenvalues and eigenvectors
  • Follow the steps and examples provided in the tutorials
  • Try solving practice problems related to eigenvalues and eigenvectors
Develop a Presentation on Linear Transformations
Creating a presentation on linear transformations provides an opportunity to synthesize knowledge, explain concepts, and improve communication skills covered in Module 2.
Browse courses on Linear Transformations
Show steps
  • Research and gather information on linear transformations
  • Organize the content into a logical flow
  • Design slides with clear and concise explanations
  • Practice presenting the material
Solve Practice Problems on Singular Value Decomposition
Solving practice problems on singular value decomposition can reinforce understanding and improve problem-solving skills covered in Module 5.
Browse courses on Singular Value Decomposition
Show steps
  • Find practice problems on singular value decomposition
  • Attempt to solve the problems using the concepts learned in the course
  • Review and correct your solutions against the provided answers or consult with others
Participate in Linear Algebra Competitions
Participating in competitions can challenge understanding, foster problem-solving skills, and provide recognition for excellence in linear algebra, which is related to the topics covered in this course.
Browse courses on Linear Algebra
Show steps
  • Research and find suitable linear algebra competitions
  • Practice solving problems and prepare for the competition
  • Participate in the competition and strive for success
Contribute to Open-Source Projects on Linear Algebra
Contributing to open-source projects allows for practical application of linear algebra concepts, exposure to real-world challenges, and collaboration with others in the field.
Browse courses on Linear Algebra
Show steps
  • Identify open-source projects related to linear algebra
  • Review the project documentation and codebase
  • Identify a suitable area to contribute
  • Submit a code contribution or issue report

Career center

Learners who complete Linear Algebra Basics will develop knowledge and skills that may be useful to these careers:
Data Scientist
Data Scientists use linear algebra to solve complex problems in various industries, including finance, healthcare, and manufacturing. This course can help build a foundation in linear algebra, which is essential for understanding and applying machine learning algorithms. The course covers topics such as vector spaces, linear transformations, and eigenvalues, which are all fundamental concepts in data science.
See salaries and explore the career path for Data Scientist
Machine Learning Engineer
Machine Learning Engineers use linear algebra to develop and implement machine learning models. This course can help build a strong foundation in linear algebra, which is essential for understanding machine learning algorithms. The course covers topics such as vector spaces, linear transformations, and eigenvalues, which are all fundamental concepts in machine learning.
See salaries and explore the career path for Machine Learning Engineer
Quantitative Analyst
Quantitative Analysts use linear algebra to model and analyze financial data. This course can help build a strong foundation in linear algebra, which is essential for understanding and applying quantitative analysis techniques. The course covers topics such as vector spaces, linear transformations, and eigenvalues, which are all fundamental concepts in quantitative analysis.
See salaries and explore the career path for Quantitative Analyst
Actuary
Actuaries use linear algebra to model and analyze insurance and financial data. This course can help build a strong foundation in linear algebra, which is essential for understanding and applying actuarial techniques. The course covers topics such as vector spaces, linear transformations, and eigenvalues, which are all fundamental concepts in actuarial science.
See salaries and explore the career path for Actuary
Financial Analyst
Financial Analysts use linear algebra to model and analyze financial data. This course can help build a strong foundation in linear algebra, which is essential for understanding and applying financial analysis techniques. The course covers topics such as vector spaces, linear transformations, and eigenvalues, which are all fundamental concepts in financial analysis.
See salaries and explore the career path for Financial Analyst
Operations Research Analyst
Operations Research Analysts use linear algebra to optimize business processes. This course can help build a strong foundation in linear algebra, which is essential for understanding and applying operations research techniques. The course covers topics such as vector spaces, linear transformations, and eigenvalues, which are all fundamental concepts in operations research.
See salaries and explore the career path for Operations Research Analyst
Software Engineer
Software Engineers use linear algebra to develop and implement software algorithms. This course may be useful for building a foundation in linear algebra, which can be helpful for understanding and applying software algorithms. The course covers topics such as vector spaces, linear transformations, and eigenvalues, which are all fundamental concepts in software engineering.
See salaries and explore the career path for Software Engineer
Computer Scientist
Computer Scientists use linear algebra to develop and implement computer algorithms. This course may be useful for building a foundation in linear algebra, which can be helpful for understanding and applying computer algorithms. The course covers topics such as vector spaces, linear transformations, and eigenvalues, which are all fundamental concepts in computer science.
See salaries and explore the career path for Computer Scientist
Mathematician
Mathematicians use linear algebra to solve complex mathematical problems. This course may be useful for building a foundation in linear algebra, which can be helpful for understanding and applying mathematical concepts. The course covers topics such as vector spaces, linear transformations, and eigenvalues, which are all fundamental concepts in mathematics.
See salaries and explore the career path for Mathematician
Physicist
Physicists use linear algebra to model and analyze physical systems. This course may be useful for building a foundation in linear algebra, which can be helpful for understanding and applying physical concepts. The course covers topics such as vector spaces, linear transformations, and eigenvalues, which are all fundamental concepts in physics.
See salaries and explore the career path for Physicist
Economist
Economists use linear algebra to model and analyze economic systems. This course may be useful for building a foundation in linear algebra, which can be helpful for understanding and applying economic concepts. The course covers topics such as vector spaces, linear transformations, and eigenvalues, which are all fundamental concepts in economics.
See salaries and explore the career path for Economist
Statistician
Statisticians use linear algebra to analyze data. This course may be useful for building a foundation in linear algebra, which can be helpful for understanding and applying statistical concepts. The course covers topics such as vector spaces, linear transformations, and eigenvalues, which are all fundamental concepts in statistics.
See salaries and explore the career path for Statistician
Teacher
Teachers use linear algebra to teach mathematics and other subjects. This course may be useful for building a foundation in linear algebra, which can be helpful for understanding and teaching mathematical concepts. The course covers topics such as vector spaces, linear transformations, and eigenvalues, which are all fundamental concepts in mathematics education.
See salaries and explore the career path for Teacher
Consultant
Consultants use linear algebra to solve problems in various industries. This course may be useful for building a foundation in linear algebra, which can be helpful for understanding and applying consulting techniques. The course covers topics such as vector spaces, linear transformations, and eigenvalues, which are all fundamental concepts in consulting.
See salaries and explore the career path for Consultant
Financial Advisor
Financial Advisors use linear algebra to manage and invest money. This course may be useful for building a foundation in linear algebra, which can be helpful for understanding and applying financial planning techniques. The course covers topics such as vector spaces, linear transformations, and eigenvalues, which are all fundamental concepts in financial planning.
See salaries and explore the career path for Financial Advisor

Reading list

We've selected 15 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 Basics.
Linear Algebra and Its Applications
Save
Provides a comprehensive introduction to linear algebra, covering topics such as vector spaces, linear transformations, and matrices. It valuable resource for students who want to learn more about the mathematical concepts behind machine learning and data science.
Linear Algebra and Its Applications
Paperback
Check
Linear Algebra and Its Applications
Kindle Edition
Check
Cover image
Deep Learning
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Comprehensive introduction to deep learning, covering topics such as convolutional neural networks, recurrent neural networks, and generative adversarial networks. It valuable resource for students who want to learn more about the latest developments in machine learning.
Deep Learning
Paperback
$$$
Deep Learning (Adaptive Computation and Machine...
Hardcover
$$$
Deep Learning (Adaptive Computation and Machine...
Kindle Edition
$$$
Cover image
Reinforcement Learning, second edition
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Comprehensive introduction to reinforcement learning, covering topics such as Markov decision processes, value function approximation, and policy gradient methods. It valuable resource for students who want to learn more about the practical applications of machine learning.
Reinforcement Learning, second edition: An...
Hardcover
$$$
Reinforcement Learning, second edition: An...
Kindle Edition
$$$
Cover image
Speech and Language Processing. An Introduction to...
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Comprehensive introduction to natural language processing, covering topics such as part-of-speech tagging, parsing, and machine translation. It valuable resource for students who want to learn more about the practical applications of machine learning in natural language processing.
Speech and Language Processing An Introduction to...
Paperback
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Cover image
Computer Vision
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Comprehensive introduction to computer vision, covering topics such as image formation, feature extraction, and object recognition. It valuable resource for students who want to learn more about the practical applications of machine learning in computer vision.
Computer Vision
Paperback
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Computer Vision
Kindle Edition
Check
Cover image
Matrix Mathematics
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Comprehensive introduction to matrix analysis, covering topics such as matrix norms, eigenvalues, and eigenvectors. It valuable resource for students who want to learn more about the mathematical foundations of machine learning and data science.
Matrix Mathematics: A Second Course in Linear...
Hardcover
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Matrix Mathematics: A Second Course in Linear...
Kindle Edition
$$$
Cover image
Introduction to Applied Linear Algebra
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Comprehensive introduction to convex optimization, covering topics such as linear programming, semidefinite programming, and conic programming. It valuable resource for students who want to learn more about the mathematical foundations of machine learning and data science.
Introduction to Applied Linear Algebra: Vectors,...
Hardcover
$$
Introduction to Applied Linear Algebra: Vectors,...
Kindle Edition
$$
Machine Learning
Save
Comprehensive introduction to machine learning, covering topics such as supervised learning, unsupervised learning, and reinforcement learning. It valuable resource for students who want to learn more about the practical applications of machine learning.
Machine Learning (McGraw-Hill International...
Paperback
$$$
Cover image
Data Science for Business
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Comprehensive introduction to data science, covering topics such as data mining, data visualization, and data analysis. It valuable resource for students who want to learn more about the practical applications of data science in business.
Data Science for Business: What You Need to Know...
Paperback
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Data Science for Business: What You Need to Know...
Kindle Edition
$$
Cover image
The Elements of Statistical Learning
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Comprehensive introduction to statistical learning, covering topics such as linear regression, logistic regression, and tree-based methods. It valuable resource for students who want to learn more about the mathematical foundations of machine learning.
The Elements of Statistical Learning: Data Mining,...
Hardcover
$$$
The Elements of Statistical Learning: Data Mining,...
Hardcover
$$$
The Elements of Statistical Learning: Data Mining,...
Kindle Edition
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Pattern Recognition and Machine Learning
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Comprehensive introduction to pattern recognition and machine learning, covering topics such as supervised learning, unsupervised learning, and reinforcement learning. It valuable resource for students who want to learn more about the practical applications of machine learning.
Pattern Recognition and Machine Learning...
Hardcover
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Pattern Recognition and Machine Learning...
Paperback
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Pattern Recognition and Machine Learning (text...
Unknown Binding
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Introduction to Linear Algebra
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Classic introduction to linear algebra, written by one of the world's leading experts in the field. It great resource for students who want to learn the basics of linear algebra in a clear and concise way.
Introduction to Linear Algebra (Gilbert Strang)
Hardcover
$$$$
Cover image
Linear Algebra: A Modern Introduction
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Modern introduction to linear algebra, written in a clear and engaging style. It great resource for students who want to learn about the latest developments in linear algebra.
Linear Algebra: A Modern Introduction
Hardcover
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Linear Algebra: A Modern Introduction
Kindle Edition
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Linear Algebra: A Modern Introduction (Available...
Hardcover
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Linear Algebra: A Modern Introduction (with CD-ROM)...
Hardcover
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Student Solutions Manual for Poole's Linear Algebra...
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Hands-On Machine Learning with Scikit-Learn, Keras,...
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Comprehensive introduction to machine learning, written with a focus on practical applications. It great resource for students who want to learn more about the practical applications of machine learning.
Hands-On Machine Learning with Scikit-Learn, Keras,...
Paperback
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Hands-On Machine Learning with Scikit-Learn, Keras,...
Paperback
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Hands-On Machine Learning with Scikit-Learn, Keras,...
Kindle Edition
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Cover image
Linear Algebra Done Right
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More advanced treatment of linear algebra, written for students who have already taken a basic course in the subject. It covers topics such as abstract vector spaces, linear operators, and multilinear algebra.
Linear Algebra Done Right (Undergraduate Texts in...
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Linear Algebra Done Right (Undergraduate Texts in...
Kindle Edition
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Linear Algebra Done Right (Undergraduate Texts in...
Hardcover
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Linear Algebra Done Right (Undergraduate Texts in...
Paperback
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(Español) Aljebra lineala ondo egina
Paperback
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Course image
Effort
21 hours to complete
Level
Intermediate
Via
Coursera
Institution
IIT Roorkee
Instructor
Dr. S. K. Gupta
Language
English
Traffic lights
Read about what's good
what should give you pause
and possible dealbreakers
Taught by Dr. S. K. Gupta, who is recognized for their work in the field of machine learning and data science
Builds a strong foundation for beginners in linear algebra, which is a core skill for machine learning and data science
Covers the mathematical concepts related to linear algebra, which include vector spaces, subspaces, linear span, basis, and dimension
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