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What would you suggest as a complimentary resource to this?
by victor106 5mo ago
What would you suggest as a complimentary resource to this?
- isomorphic 5mo agoI think GP is both referring to and suggesting: https://linear.axler.net/ https://linear.axler.net/
- srean 5mo agoThis is a great book but and as the author himself notes, it's not an ideal first linear algebra book. Strang can be great as a first book. He focuses more on what rather than why, so if one wants to delve deeper, it needs to be supplemented by a few other books.
- mamonster 5mo agoI still don't get why Axler decided to discuss the Jordan normal form after already doing the spectral theorem, it's a bit like presenting Riemannian integration after Lebesgue. For the long term his emphasis on operators is probably better as naturally transitions into functional analysis, but you can get a lot of stuff done without ever touching them.
- KalMann 5mo agoDid you misstate your comment? The Jordan normal form is more general than spectral decomposition so it should come after.
- mamonster 5mo agoI'm open to being corrected, but AFAIK the normal form (1870) precedes the official focus on operators (with Hilbert) by like 20-30 years.
- srean 5mo agoKalMann is correct. Jordan canonical form decomposition is more general. Every matrix in an algebraically closed field will have such a decomposition. This is not true for spectral decomposition. Only diagonalizable matrices will have a spectral decomposition and they are a smaller subset. That said, Jordan form is uglier than spectral decomposition, to my taste that is. Spectral decomposition so beautiful and neat.
- Koshkin 5mo agoAlso: https://lew98.github.io/Mathematics/LADR_Solutions/LADR_Solutions.pdf https://lew98.github.io/Mathematics/LADR_Solutions/LADR_Solu...