Complete linear algebra: theory and implementation in code (updated 2/2022)

Learn concepts in linear algebra and matrix analysis, and implement them in MATLAB and Python.

What you'll learn
Understand theoretical concepts in linear algebra, including proofs
Implement linear algebra concepts in scientific programming languages (MATLAB, Python)
Apply linear algebra concepts to real datasets
Ace your linear algebra exam!
Apply linear algebra on computers with confidence
Gain additional insights into solving problems in linear algebra, including homeworks and applications
Be confident in learning advanced linear algebra topics
Understand some of the important maths underlying machine learning
* Manually corrected closed-captions *

Requirements
Basic understanding of high-school algebra (e.g., solve for x in 2x=5)
Interest in learning about matrices and vectors!
(optional) Computer with MATLAB, Octave, or Python (or Jupyter)
Description
You need to learn linear algebra!

Linear algebra is perhaps the most important branch of mathematics for computational sciences, including machine learning, AI, data science, statistics, simulations, computer graphics, multivariate analyses, matrix decompositions, signal processing, and so on.

You need to know applied linear algebra, not just abstract linear algebra!

The way linear algebra is presented in 30-year-old textbooks is different from how professionals use linear algebra in computers to solve real-world applications in machine learning, data science, statistics, and signal processing. For example, the "determinant" of a matrix is important for linear algebra theory, but should you actually use the determinant in practical applications? The answer may surprise you, and it's in this course!

If you are interested in learning the mathematical concepts linear algebra and matrix analysis, but also want to apply those concepts to data analyses on computers (e.g., statistics or signal processing), then this course is for you! You'll see all the maths concepts implemented in MATLAB and in Python.

Unique aspects of this course

Clear and comprehensible explanations of concepts and theories in linear algebra.

Several distinct explanations of the same ideas, which is a proven technique for learning.

Visualization using graphs, numbers, and spaces that strengthens the geometric intuition of linear algebra.

Implementations in MATLAB and Python. Com'on, in the real world, you never solve math problems by hand! You need to know how to implement math in software!

Beginning to intermediate topics, including vectors, matrix multiplications, least-squares projections, eigendecomposition, and singular-value decomposition.

Strong focus on modern applications-oriented aspects of linear algebra and matrix analysis.

Intuitive visual explanations of diagonalization, eigenvalues and eigenvectors, and singular value decomposition.

Improve your coding skills! You do need to have a little bit of coding experience for this course (I do not teach elementary Python or MATLAB), but you will definitely improve your scientific and data analysis programming skills in this course. Everything is explained in MATLAB and in Python (mostly using numpy and matplotlib; also sympy and scipy and some other relevant toolboxes).

Benefits of learning linear algebra

Understand statistics including least-squares, regression, and multivariate analyses.

Improve mathematical simulations in engineering, computational biology, finance, and physics.

Understand data compression and dimension-reduction (PCA, SVD, eigendecomposition).

Understand the math underlying machine learning and linear classification algorithms.

Deeper knowledge of signal processing methods, particularly filtering and multivariate subspace methods.

Explore the link between linear algebra, matrices, and geometry.

Gain more experience implementing math and understanding machine-learning concepts in Python and MATLAB.

Why I am qualified to teach this course

I have been using linear algebra extensively in my research and teaching (in MATLAB and Python) for many years. I have written several textbooks about data analysis, programming, and statistics, that rely extensively on concepts in linear algebra.

So what are you waiting for??

Watch the course introductory video and free sample videos to learn more about the contents of this course and about my teaching style. If you are unsure if this course is right for you and want to learn more, feel free to contact with me questions before you sign up.

I hope to see you soon in the course!

Mike

Who this course is for
Anyone interested in learning about matrices and vectors
Students who want supplemental instruction/practice for a linear algebra course
Engineers who want to refresh their knowledge of matrices and decompositions
Biologists who want to learn more about the math behind computational biology
Data scientists (linear algebra is everywhere in data science!)
Statisticians
Someone who wants to know the important math underlying machine learning
Someone who studied theoretical linear algebra and who wants to implement concepts in computers
Computational scientists (statistics, biological, engineering, neuroscience, psychology, physics, etc.)
Someone who wants to learn about eigendecomposition, diagonalization, and singular value decomposition!