Pairwise squared distances

Question

Implement squared Euclidean distances between rows of finite matrices A and B without creating a three-dimensional difference tensor. Address tiny negative round-off.

Short answer

Expand the squared norm into row norms and a matrix product. Floating-point cancellation can yield tiny negative values, which are clipped to zero. Large-magnitude nearly identical vectors may still need a more stable direct calculation.

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Lessons behind this question

The Supervised Learning Problem and the ML Pipeline
Matrix Algebra: Operations, Rules, and the Transpose
Kernel, Image, and the Rank-Nullity Theorem

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