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What are useful books on Linear ALgebra? I need theoretical , abstract approach but most of the proofs are explained with detail. In general how can we improve our linear algebra knowledge to solve problems in Putnam Competition or similar Competition programs ?

Analysis
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I use Elementary Linear Algebra, $11^{th}$ Edition by Howard Anton (Professor Emeritus, Drexel University) and Chris Rorres (University of Pennsylvania).

This, to me, is a very nice book when starting with Linear Algebra.

user860374
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