A Crash Course in Applied Linear Algebra
summary
Shows concrete claims and runnable tools: y = Ax decomposition as a unifying model, practical demos in NumPy, and when low matrix rank yields compression and speedups. Explains singular value decomposition and the Moore–Penrose pseudo-inverse with exact interpretations (least squares or minimum-norm solutions). Uses eigenvalues to predict stability and Markov chains to illustrate steady states, and builds a control example that steers a 2D head to a target with no overshoot.
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chapters (9)
- 0:00Linear algebra in data prediction
- 1:50Why linear algebra matters
- 8:27Matrix rank applications
- 12:23Eigenvalues and eigenvectors
- 17:02Markov chains and evolution
- 22:39Singular value decomposition
- 26:32Pseudoinverse practical uses
- 30:34Hard disk control problem
- 33:43Summary
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