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Linear algebra resources and links of interest
Online courses
Linear algebra
Khan Academy: Linear Algebra
Not really a stand alone linear algebra class (more as a supplement), but contains lots of good information.
Open Courseware: Linear Algebra
MIT’s introductory linear algebra course.Statistics for Applications (18.650/18.6501)
- Principal Component Analysis (cont.)(Lecture 20)
Open Courseware: Matrix Methods i n in Data Analysis, Signal Processing, and Machine Learning
The follow-on course to the introduction linear algebra class. Matrix methods expands on the fundamental concepts discussed and introduces some additional ideas that are also very useful, such as positive-definite matrices, singular value decomposition, etc.
edx.org: Linear Algebra Courses
Free (or paid, if you want a certificate), self-paced linear algebra courses from a number of institutions.
Singular Value Decomposition (SVD)
SVD is a fundamental factorization technique that is used a in wide variety of situations and fields that vary from statistics (e.g., principal component analysis) to fluid flow (e.g., dynamical systems).
Steve Brunton
Singular Value Decomposition YouTube playlist
Book associated with lectures: Data Driven Science & Engineering: Machine Learning, Dynamical Systems, and Control
Notes
I (Jason) have been really enjoying this playlist. Great explanations of SVD with coding examples (Matlab and Python) and applications (e.g., image compression, fast approximations of fluid flow, PCA).
What may be of particular interest to some in this group is discussion of Robust Principal Component Analysis (RPCA), which is a means of dealing with matrices that are missing lots of data.
Principal Component Analysis (PCA)
A specific application of SVD focused on finding the rotation of a matrix that maximizes the most variation along a set of axes (columns) that have been standardized.
MIT’s Open Courseware
Videos highlighting applications of linear algebra
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Zach Star
PCA
Luis Serrano
Principal Component Analysis (PCA)
One of the better explanations of PCA I’ve seen.
StatQuest with Josh Starmer (Genetics Dept., University of North Carolina at Chapel Hill)
Nice explanations of (among other things):
Scaling: so as not to artificially weight data measured at different scales.
Centering: SVD expects data at the origin, so PCA expects data to be centered at the origin.
STHDA
Data4Bio
Julia Silge
Code Emporium
Principal Component Analysis (PCA) - The Math You Should Know!
A deep dive into the mathematical justification of PCA.
Luis Serrano
Principal Component Analysis (PCA)
One of the best explanations of PCA I’ve seen.