TITLE: Looking for a different type of Linear Algebra book
QUESTION [6 upvotes]: Are there any good linear algebra books with lots of (mathematical, preferably algebraic or geometric-flavored) applications?
E.g. I'm not so interested in the typical engineering-style applications or even really analysis-style (not that I would be upset by interesting ones) applications since I feel like those are very commonly covered many books, but if it contained computing homology or graph theory or combinatorics or etc... that would be awesome!
I'm comparing against things like Axler, Hoffman/Kunze, Strang, Friedberg/Insel/Spence, which all seem to have very same-y treatments of linear algebra with no super exciting exercises to keep young math students excited!

REPLY [2 votes]: Here are a couple I found as well.
Computational Linear & Commutative Algebra looks like there are a lot of heavily algebraic-geometric flavored applications of linear algebra. And actually, this is the 3rd in the series, the other two books are just called Computational Commutative Algebra 1/2, but I'm guessing there is quite a bit of linear algebra in use too, and they have a lot of "tutorials" where they cover e.g. polytopes, graph colorings, varieties, chess puzzles, error correcting codes, and much more.
And, there's no homology theory here, but Artin's Algeba of course makes heavy use of linear algebra and matrix groups throughout the text with plenty of fun, challenging exercises.
Neither one, of course, is a replacement for  a first class in theoretical linear algebra (actually, maybe Artin could be used this way... maybe), but I think that's ok.