Ok, so Hefferon was my textbook for 2 full semesters. Lots of problems with this book. Hefferon is an algebraist, so the computational aspect of linear algebra ie. the stuff you are most likely to use linalg for at your workplace, has been given short shrift. Instead, the author gives fullblown treatment to theorem proving in vector spaces. So you are spending a lot of time constructing isomorphisms between subspaces....that shit is neat for a math major, which I was, but now that I'm in the workplace, I find what the world calls "linear algebra" isn't what Hefferon cares about.

eg. One of the basics you must absolutely know, or so I've been told, is how to do a PCA, and why a PCA is not the same as regression. So if you've got multidimensional data, say data in 7 dimensions ( risk ratio, fico score, salary, age etc etc ), you want to know if you can reduce that whole set to say 1 dimension. ie. can you transform the original set of 7 variable vectors into a much smaller set of 1 variable vectors that captures 90% of the information in the original ? If so, how ? Turns out you construct a linear combination of correlated variables. Ok, but there's infinitely many combinations. So how ? Well, construct it in such a fashion that the variance of the combination is maximized. That component is called the Principal Component, and its the single most used technique to reduce dimensionality in the industry. So you've taken a 7-dimension space and nicely reduced it to a 1-dimension subspace with maximum variance that explains 90% of the original 7 dimension space. Its quite amazing actually. http://en.wikipedia.org/wiki/Principal_component_analysis

Similarly, there are a whole bunch of very common stuff you'd actually use linear algebra for in CG - translation, rotation in 3D, shear matrices and the like. Hefferon doesn't do those either.

In portfolio theory which is my bread and butter (http://en.wikipedia.org/wiki/Portfolio_theory ) almost everything I do is very properly linear algebra. But again, Hefferon doesn't offer any insight into how/why finding a vector with minimum variance can yield better returns in a vector space of portfolios.