Complete linear algebra: theory and implementation
What you will 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 closedcaptions *
Curriculum
Section 1: Introductions
Section 2: Vectors
Section 3: Introduction to matrices
Section 4: Matrix multiplications
Section 5: Matrix rank
Section 6: Matrix spaces
Section 7: Solving systems of equations
Section 8: Matrix determinant
Section 9: Matrix inverse
Section 10: Projections and orthogonalization
Section 11: Leastsquares for modelfitting in statistics
Section 12: Eigendecomposition
Section 13: Singular value decomposition
Section 14: Quadratic form and definiteness
Course Description
Learn concepts in linear algebra and matrix analysis, and implement them in MATLAB and Python.
Requirements
 Basic understanding of highschool 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, and so on.
You need to know applied linear algebra, not just abstract linear algebra!
The way linear algebra is presented in 30yearold textbooks is different from how professionals use linear algebra in computers to solve realworld applications. 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, then this course is for you!
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, leastsquares projections, eigendecomposition, and singularvalue decomposition.
 Strong focus on modern applicationsoriented aspects of linear algebra and matrix analysis.
 Intuitive visual explanations of diagonalization, eigenvalues and eigenvectors, and singular value decomposition.
Benefits of learning linear algebra
 Understand statistics including leastsquares, regression, and multivariate analyses.
 Improve simulations in engineering, computational biology, finance, and physics.
 Understand data compression and dimensionreduction (PCA, SVD, eigendecomposition).
 Understand the math underlying machine learning and linear classification algorithms.
 Explore the link between linear algebra, matrices, and geometry.
Why I am qualified to teach this course:
I have been using linear algebra extensively in my research and teaching (primarily in MATLAB) 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!