Cohen teaches linear algebra by writing it: vectors, matrices, rank, least squares, decompositions, and the implementation of each in Python. He does not prove, he shows. This is what you open once you have understood the idea and have to make it work.
What I took from it
The numerical side, which in theoretical books turns up as a footnote and here takes the centre: what happens when a matrix is close to not being invertible. It sounds remote and it is an everyday problem. When a forecasting model returns enormous coefficients with signs that make no sense, the usual cause is not missing data: it is that two of the variables say the same thing, the system becomes unstable, and the result blows up. The fix is to drop one, not to gather more data.
Out of that came a check I run before accepting any model built by someone else: look for columns that are combinations of other columns. In business data it happens constantly, because systems store the same fact three times under different names — the total, the net and the tax; the cost, the margin and the price.
The second thing is the singular value decomposition as a working tool rather than an exam topic: it is what sits under reducing dimensions, under compression, and under much of search by meaning.
What I left out
The long exercises and the implementation detail, because in practice you call a library. And a warning about the copy I have, which is an early release: it has a draft's rough edges, uneven chapters and half-polished examples. If someone is going to read only one of the two linear algebra books, read Strang to understand and open this one when there is code to write.