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DelftX: Linear Algebra II: Matrices and Linear Transformations

This course provides an overview of bachelor-level linear algebra. You will review all the concepts and practice and refresh the skills related to matrices and linear transformations.

Linear Algebra II: Matrices and Linear Transformations
6 weeks
4–6 hours per week
Self-paced
Progress at your own speed
Free
Optional upgrade available

Choose your session:

After a course session ends, it will be archivedOpens in a new tab.
Starts Apr 17
Ends May 31
Starts Jul 3

About this course

Skip About this course

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 course
This 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.

At a glance

  • Institution: DelftX
  • Subject: Math
  • Level: Intermediate
  • Prerequisites:

    Prior knowledge of all the material covered.

    This is a self-contained bachelor-level course. However, we do assume that you are familiar with standard high school mathematics, specifically standard functions and their properties, algebraic manipulation of equations and inequalities and standard mathematical notation.

    This course is a review course. As such the course requires you to have studied linear algebra in the past or at least to be familiar with its course contents. If this is not the case for you, then you can still do the course, but be prepared for a high pace!

  • Language: English
  • Video Transcripts: اَلْعَرَبِيَّةُ, Deutsch, English, Español, Français, हिन्दी, Bahasa Indonesia, Português, Kiswahili, తెలుగు, Türkçe, 中文
  • Associated programs:
  • Associated skills:Machine Learning, Eigenvalues And Eigenvectors, Linear Algebra, Basic Math, Quantum Computing, Matrix Algebra

What you'll learn

Skip What you'll learn
  • 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.

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

Frequently Asked Questions

Skip Frequently Asked Questions

Q: I am going to start a master’s in engineering. Is this MOOC mandatory?
A: It is not mandatory, but we believe it could be useful to revisit some of these topics.

Q: Can I use the certificate I get from this MOOC to get an exemption from a certain course?
A: No, you cannot. That is not the goal of these courses.

Q: Can I use this MOOC as a substitute for the Bridging Programme (Schakelprogramma)?
A: No, you cannot.

Q: What level is required to follow this course?
A: It is a review course. Hence the pace will be a bit higher than when you learn about these topics for the first time. However, every concept within linear algebra will be explained.

Q: What is the duration of this course?
A: You will probably need 4 to 6 hours per week, for 6 weeks.

Q: I am going to follow this MOOC. Will I have to hand in homework?
A: No. The exercises will be checked automatically, and you will get immediate feedback.

This course is part of Mastering Linear Algebra Professional Certificate Program

Learn more 
Expert instruction
2 skill-building courses
Self-paced
Progress at your own speed
3 months
4 - 6 hours per week

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