Vector Norms Measure Size, Not Meaning
Calculate L1, L2, and L-infinity vector norms, verify their defining rules, and see what an embedding magnitude can—and cannot—tell you.
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Subspaces for AI: Test Restricted Feature Families
Learn the subspace test, prove that a plane is closed under vector operations, and use NumPy to inspect lower-dimensional representation directions.
Vector Addition for AI: How Residual Updates Combine Signals
Learn vector addition component by component, explore its parallelogram geometry, and catch shape, broadcasting, and feature-alignment mistakes in NumPy.
Linear Equations for AI: Turn One Formula Into a Geometric Line
Learn how one two-variable linear equation becomes a line, test its points, handle vertical cases, and read a linear classifier score contour.