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Example 11: PCA via SVD: explained variance ratio
Example 12: Least squares fit and residual norm
Example 13: Solving SPD system with Cholesky
Example 14: Condition number predicts sensitivity
Example 15: Sparse adjacency matvec (pure NumPy COO)
Example 16: Attention block computation (QK^T then AV)
Example 17: Vector space closure + centering as a subspace projection
Example 18: Predictions and attention are in spans
Example 19: One-hot basis vectors and coordinate representations
Example 1: Vector space closure + centering as a subspace projection
Example 20: Linear layers and backprop are linear maps + adjoints
Example 21: Dot products, norms, and cosine similarity (retrieval)
Example 22: Least squares residual is orthogonal to column space
Example 23: Null space explains non-identifiability (overparameterized linear model)
Example 24: Power iteration for dominant eigenvector (PCA direction)
Example 25: PSD checks: covariance and kernel Gram matrices
Example 26: SVD factorization and best rank-1 reconstruction
Example 27: PCA via SVD: explained variance ratio
Example 28: Least squares fit and residual norm
Example 29: Solving SPD system with Cholesky
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