- Coding the Matrix, Klein
This has a strong emphasis on LA's utility in CS, and includes concepts outside traditional LA that enrich the narrative.
- Intro to Linear Algebra, Strang
Strang approaches LA from a practical less-theoretical angle, which makes it very sensible if you're an engineer but may not be as suitable if you're a mathematician.
- Linear Algebra, A Modern Intro, Poole
This is a solid text that has worked out most of its bugs over the editions.
- Linear Algebra and its Applications, Lay
Like Poole, this is also a solid and long running text.
The books by Klein and Strang also benefit from free videos of those courses that are available from Coursera/BrownU and MIT OCW. Klein's is also available on the Kindle.
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