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Im looking for a linear algebra textbook that meets two criterion:

  1. The book should be proof-based.

  2. The book should try and motivate most, if not most of the ideas, of the geometry of linear maps and matrix decompositions. For example, the permutation maps can be thought of as rotation maps because permutation matrices simply rotate the basis vectors. I’m looking for a book that explains all ideas and methods geometrically as well. A plus would also be that the book also foreshadows which properties can be generalized to a functional analytic setting.

Junaid Aftab
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    Linear algebra done right by axler , algebra by artin and opinion based question – Cloud JR K Dec 05 '18 at 19:16
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    This very nearly describes almost every recommendation for a linear algebra book I've seen on the site. Of which, there are dozens. You should search before asking... – rschwieb Dec 05 '18 at 20:31

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