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B08 A SMALL STEP SIDEWAYS

Directions, eigenvectors, and low-rank structure

Some directions a matrix only stretches, never turns. Find them in a 2×2 example, then see how keeping only the strongest ones powers PCA and LoRA fine-tuning.

LESSON OVERVIEW10 min lesson

Lesson overview

Some directions a matrix only stretches, never turns. Find them in a 2×2 example, then see how keeping only the strongest ones powers PCA and LoRA fine-tuning.

What you’ll explore

  • Find an eigenvalue by checking Av = λv, describe the SVD as rotate-stretch-rotate, and count the numbers saved by a low-rank factorization.
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Original explanations, connected to the research.

Deep Learning — linear algebra
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