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Linear algebra is one of the most useful subjects I've ever learned. And not just because it's practical (though it is enormously so, showing up all branches of science and engineering) but for a surprisingly mundane abstract observation:
an arbitrarily complex object (a "vector") can be described in terms of a simpler set of objects ("the basis set"). This simple abstraction shows up almost everywhere. Want to compress images? Describe it in terms of a smaller set of Fourier components.
With some abuse of notation, this abstraction can be expanded even further. What's deep learning? Take complicated, very high dimensional data (e.g., input images) and use DL and back propagation to discover a simpler representation of it to do all sorts of practical tasks.
That's why I was psyched to see this book: "Thirty-three Miniatures: Mathematical and Algorithmic Applications of Linear Algebra". It's a set of short vignettes that shows the various places that LA shows up. kam.mff.cuni.cz/~matousek/stml… (ht: @newsycombinator)
Despite its power, LA is treated as "just matrix multiplication" or a speed bump on the way to harder math. But LA is beautiful in its own right, something that I came to appreciate in Gene Golub's lectures. Let's give it the respect it deserves! en.wikipedia.org/wiki/Gene_H._G…
