Unit 2 of 15
Linear Algebra and Calculus for Learning
- 4 lessons
- Videos 11 to 14
Most learning methods are built from vectors, matrices and derivatives. This unit teaches the linear algebra and calculus the course needs, from linear predictions and projections to gradient descent.
A data table becomes a design matrix with one row per observation, and a coefficient vector turns it into one prediction per row, with every dimension checked. Span, rank and orthogonal projection decide which predictions a linear model can produce and when its coefficients are unique. Derivatives, partial derivatives and the chain rule show how a loss changes with each parameter. Gradient descent uses them to step downhill, the step size decides whether the iterations converge or diverge, and convexity and the Hessian describe the shape of the objective.
Every lesson will be one video. The videos are coming soon, and each lesson page already has the definitions and an example for every key term.
Linear Algebra for Predictions
Vectors, Matrices, and Linear Predictions
How a feature vector and a coefficient vector give one prediction through a dot product, and how a design matrix with an intercept column gives a whole vector of linear predictions with matching dimensions.
Video 11
Vector Geometry, Rank, and Projection
How the Euclidean norm and orthogonal projection find the closest prediction a linear model can make, and how span, column space, rank, singular matrices and conditioning decide whether its coefficients are unique and stable.
Video 12
Calculus for Optimization
Derivatives, Partial Derivatives, and the Chain Rule
How derivatives, partial derivatives and the gradient measure how a loss changes with each parameter, how the chain rule tracks every factor of a prediction error, and how directional derivatives and finite differences check it.
Video 13
Gradient Descent and Optimization
How gradient descent steps against the gradient of an objective function, how the learning rate decides convergence, and how stationary points, local and global minima, convexity and the Hessian describe where it can stop.
Video 14