Singular Value Decomposition

The Swiss army knife of matrix decompositions

SVD decomposes any matrix (not just square ones) into three factors: U * Sigma * V^T. The singular values in Sigma tell you how much 'information' each component carries. By keeping only the top-k singular values, you get the best rank-k approximation -- this is the mathematical foundation of image compression, latent semantic analysis, and (crucially) LoRA fine-tuning. This module builds from the geometry of SVD to hands-on applications. Mini-lab: Compress a photo by keeping only the top-k singular values. Watch the image degrade as you reduce k from 100 to 10 to 1.

Estimated time: 60 minutes

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