singular value decomposition


Summary

SVD

be careful of the number of rows and cols

Process

Concept

Singular matrices

  • transformation that may add or remove dimensions

Singular value decomposition

  • diagonalization of non-square(and singular) matrcies
  • using the product with transpose to create a symmetric matrix, on which orthogonal diagonalization can be done

we want to be like the psuedo-eigenvectors of

Relation to polar decomposition

Application

SVD by transpose product

pain

Extra

Octave

octave
# SVD of a matrix
[U, S, V] = svd(A)