Determinants: signed area, volume, and collapsed directions
Calculate a determinant, see how its sign records orientation, and connect zero area to singular matrices. Learn why a small determinant alone does not imply poor conditioning.
Writing
Clear accounts of what was tried and learned.
Explanations, tutorials, build notes, and essays grounded in work that can be examined. Explore a concept, try an experiment, and follow the reasoning behind it.
Start with the interactive foundationsShowing 133–144 of 151 posts
The dot product: angles, projections, and robot motion
Learn the dot product with an interactive vector diagram, a worked projection example, and a robot heading calculation. Includes exercises and solutions.
Eigenvalues and eigenvectors: find the lines a matrix preserves
Understand eigenvalues through 2D transformations. Test stretching, reversal, zero eigenvalues, rotation, and repeated values, then connect them to robot error dynamics.
Gradient descent: learn the update, then test its limits
Work through gradient descent by hand, then explore learning rates, overshoot, and stationary points in an interactive experiment with Python and exercises.
Laplace distribution: model sensor error and tolerance
Learn the Laplace distribution through sensor error. Explore location, scale, density, interval probabilities, and the link between absolute error and median fitting.
Linear regression: fit a line and inspect its errors
Fit linear regression to robot sensor readings. Work through least squares, residuals, and MSE, then test an outlier with Python and exercises.
Logistic regression: turn a score into a probability
Explore logistic regression with synthetic robot observations. Calculate sigmoid probabilities and log loss, then change a threshold and inspect the confusion matrix.
Markov chains: transitions and stationary distributions
Learn Markov chains with a robot example. Explore transition matrices, stationary distributions, periodic chains, and absorbing states with an interactive model.
Matrix multiplication: calculate entries and compose transformations
Learn matrix multiplication through row-column dot products, compatible shapes, and a rotation-and-stretch experiment that shows why transformation order matters.
Matrix transpose and inverse: when do they agree?
Transpose rectangular matrices, calculate a 2×2 inverse, and test when a transpose reverses a transformation. Explore rotations, reflections, and singular maps.
A map of machine learning: tasks, signals, and models
Understand how supervised learning, self-supervision, reinforcement learning, NLP, and deep learning fit together through practical robot and language examples.
NLP: turn robot commands into token probabilities
Learn natural language processing through a small robot-command corpus. Compare tokenization, unigram and bigram counts, unseen contexts, embeddings, and evaluation.