Deep Learning Book (Bengio) linear algebra concepts are high level?

Question

I took an elementary level course in university and do not recognize some concepts in this book:

1. Stretching space (space transformation?) with eigenvalues and eignevectors

2. Singular Value Decomposition

3. Moore-Penrose Pseudoinverse

4. Trace Operator

5. Principle Components Analysis (this is an ML algorithm it says)

Even disregarding number five, how relevant are the other concepts and in which specific areas of deep learning are they applicable? Admittedly I have just started on the book itself but with limited time before classes start in September, I am wondering if I should invest the time to learn the above 4 or 5 or try to solidify my knowledge of more basic concepts.

Edit: Stretching space on p.41

stretching space

Answer 1

Elementary linear algebra classes can vary a lot in their content. For example, when they are geared toward physics and engineering majors, they tend to focus more on diagonalization, eigenvalues and stability (e.g. for applications toward ODEs). For math majors, they tend to focus on generalized eigenvalues, SVD (yet not-so-much PCA), Riesz representation, Rayleigh quotients and sometimes determinants. The topics you listed tend to more commonly occur in statistics (and therefore machine learning) and numerical linear algebra. Any decent textbooks on these topics will cover the above items. At the bare minimum, I would strongly recommend reinforcing your knowledge of statistics, because it will come in handy in most machine learning applications that you'll encounter.