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Companion webpage to the book "Mathematics For Machine Learning"
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Gram-Schmidt Orthogonalization by Gauss Elimination augmented matrix is incorrect #690

Open KarolisRam opened 2 years ago

KarolisRam commented 2 years ago

Describe the mistake Gram-Schmidt Orthogonalization by Gauss Elimination augmented matrix is incorrect OR it should mention that the basis vectors should be rows.

Location Please provide the

  1. version (bottom of page) - Draft (2021-07-29)
  2. Chapter - 3
  3. page - 79
  4. line number/equation number - paragraph after definition 3.9.

Proposed solution change [B˜B˜T|B˜ ] to [B˜TB˜|B˜T ] .

Additional context This is where it appears in the book: image

This is how it appears in Wikipedia (note the underlined "rows"): image

And this is the section from the original paper that introduces the concept and uses vectors as columns: image

Since the MML book always uses vectors as columns, the augmented matrix should be changed to the one in the original source.