Syllabus Map

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Core Idea

• Vectors represent points, directions, and parameter sets.
• Norms measure vector magnitude.
• Dot product measures alignment and similarity.

Key Formulas

Practical Notes

Feature scaling affects all norm-based comparisons.

• Unscaled features distort distance and similarity calculations.

L1 and L2 norms serve different modeling goals.

• L1 encourages sparsity; L2 gives smooth shrinkage.

Why This Matters for ML

• Similarity metrics in KNN, retrieval, and embedding search are built from dot products and norms.
• Regularisation terms in linear/logistic regression (L1, L2) are norm penalties on parameters.
• Cosine similarity is a default metric in NLP and representation-learning pipelines.
• Gradient magnitudes and clipping also use vector norms during optimization.