Scalars, Vectors, Matrices, and Tensors

URL: http://en.diveintodeeplearning.org/chapter_crashcourse/linear-algebra.html

Id like to point out a few things:

  1. In section 2.2.11. the 4th property of norms is an “if only if” statement (page 10 of Zico Kolter’s [Linear Algebra Review and Reference). As a consequence, the statement “It is possible to define a norm that gives zero norm to nonzero matrices” isn’t true.
  2. I would add a small discussion about the difference between a vector and a 1 x n or (n x 1) matrix.
  3. In section 2.2.8, you mention “When two vectors each have length one …”. I think it would be better to use “norm” instead on “length”, because otherwise it might confuse readers with the definition of “length” defined in section 2.2.3.
  4. In section 2.2.13.2, when talking about symmetric matrices, you mention “the entries below and above the diagonal are the same”, which is rather vague. It would be nice to see mentioned that symmetric matrices are square matrices.

I hope these suggestions are helpful.

Thanks! I’ve revised these based on your suggestions.
e.g.,
http://numpy.d2l.ai.s3-website-us-west-2.amazonaws.com/chapter_preliminaries/reduction-norm.html