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Can somebody recommend me any books to read that cover the following topics?

Chapter 1. Vector Spaces

  • 1.1. Solutions of Simultaneous Linear Equations
  • 1.2. Fields and Vector Spaces
  • 1.3. Product of Sets and of Vector Spaces
  • 1.4. Vector Subspaces
  • 1.5. Linear Independence and Bases
  • 1.6. Dimension of a Vector Space
  • 1.7. Linear Mappings
  • 1.8. Rank-Nullity Theorem

Chapter 2. Linear Mappings and Matrices

  • Linear Mappings $F^m → F^n$ and Matrices
  • Basic Properties of Matrices 27
  • Abstract Linear Mappings and Matrices 30
  • Change of a Matrix by Change of Basis 33

Chapter 3. Rings and Modules 37

Chapter 4. Determinants and Eigenvalues Redux 63

Chapter 6. Jordan Normal Form

  • Statement of the Jordan Normal Form and Strategy of Proof
  • The proof of Jordan Normal Form
  • Example of Jordan Normal Form
  • A Brief Explanation of the Final Step in PageRank as an Application of the Jordan
GRS
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    Hoffman, Kunze. Linear algebra – Vicfred Jan 25 '16 at 09:34
  • @Vicfred thanks, does it cover all of the topics? Or some of these – GRS Jan 25 '16 at 09:35
  • all except from the pagerank algorithm (google invented that right? maybe you can find a good explanation of it online) – Vicfred Jan 25 '16 at 09:36
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    I was going to say Hoffman & Kunze, but somebody already said so. If you're not looking for a milquetoast version of LA then that's definitely the book to read. – Gregory Grant Jan 25 '16 at 09:38
  • @Vicfred Does H&K really cover rings and modules in general? I don't think it does. – Gregory Grant Jan 25 '16 at 09:39
  • yes, thank you very much, I'll have a look at it – GRS Jan 25 '16 at 09:39
  • @GregoryGrant it mentions them... I don't think someone studying linear algebra for the first time needs more than that, most books at that level don't even mention them – Vicfred Jan 25 '16 at 09:40
  • @Vicfred Well I'd also recommend Hungerford's "Algebra" he has a really good chapter on linear algebra that goes into some greater generality than H&K.. – Gregory Grant Jan 25 '16 at 09:41
  • Hoffman and Kunze treat linear algebra from an advanced undergraduate or beginning graduate student perspective. Chapter 4 Polynomials has material on polynomials not only as vector spaces, but as algebras (and introduces a bit of their ideal theory). Chapter 5 Determinants defines them for entries in a commutative ring. So it does go into some of the abstract algebra/ring and module theory. – hardmath Jan 25 '16 at 12:24

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I have grown really fond of Axler's "Linear Algebra Done Right." It focuses more on conceptual problems and not tedious calculations, and emphasizes important concepts that come into play in other subjects later on. This covers most of what you mentioned in your post, for those that you don't find you can always read Manin's "Linear Algebra."

AnotherPerson
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