Complete notes and worked problems for every topic in the course — eigenvalues, SVD, PCA, regression, classification, and more. Built directly from Professor Ellis's course notes.
Characteristic polynomials, trace and determinant relations, diagonalization, spectral decomposition, positive definite matrices, quadratic forms, and covariance.
Graph definitions, adjacency matrix, degree matrix, Laplacian $L = D - A$, eigenvalues of $L$, number of components, Fiedler vector, and spectral clustering.
Column space, null space, RREF, rank-nullity theorem, linear independence, orthogonal bases, orthonormal bases, and orthogonal complement subspaces.
Standardized data, orthogonal projection to 1D and subspaces, normal equations, residual error, RMS, Hooke's Law, regression with/without intercept, and cross-validation.
Derivation from transpose products, left/right singular vectors, matrix spaces from SVD, low-rank approximation (Eckart-Young), polar decomposition, SVD properties.
Zero-mean data, scatter matrix, covariance eigenvalues, PCA as SVD, loading vectors, scores, explained variance, scree plot, and dimensionality reduction.
k-means algorithm, hyperplane from centroids, unit normal form, signed distance, logistic probability, confusion matrix, sensitivity/specificity, ROC curve, AUC.
Feed-forward computation, logistic activation, residual error, backpropagation term, gradient descent, weight update, Gram matrix, kernel functions (linear, quadratic, Gaussian).
Every formula from the course on one page. Eigenvalues, SVD, PCA, projection, classification, neuron — all key equations for fast last-minute review before the exam.
April 10, 2025 · 14 questions · 3 hours · Casio FX-991 only