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lect18

lect18, Thu 03/12

Applications of SVD

References for this week’s lectures

NCM Sections 10.1, 10.2, 10.10, 10.11 A very retro video, made in 1976 by the author of NCM, that visualizes the computation of the SVD.

Outline

• Singular value decomposition:
  • rank(A) = # of nonzero singular values
  • 2-norm(A) = max singular value
  • Frobenius norm of A = sqrt(sum(singular values))
  • Determinant of A = product(singular values)
  • A = sum_i (s_i * outerproduct(u_i, v_i))
• Low-rank approximation
  • Theory
  • Principal components
  • Image compression

• Computing the SVD: watch the video

• numpy/scipy routines:
  • spla.svd()