Just to clarify for the crowd, portfolio theory, at least as far as its connection to linear algebra, is the mathematics of a covariance matrix. You are talking about different ways to decompose such a matrix. There are many ways and the justification for any of these methods goes beyond linear algebra and is really a special area of finance theory more than linear algebra.
Long before reading the book, I spent a lot of time with financial modeling of all kinds, but your complaint doesn't resonate with me at all. I went on to study machine learning and found the ideas in Hefferon laid a good foundation. It might be fair to point out that is not a cookbook and you don't use it to learn how to wrangle LAPACK, but I think it's over the top to say what you just did.