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I have studied linear algebra during my bachelor's degree and Master's degree. I know the subject but not up-to the mark I want to understand linear algebra through linear transformation and specially the portion where we start decomposition of a vector space through a linear transformation. Like Jordan canonical form, primary decomposition theorem etc. There are so many great books available but I am unable to choose which one suit to my problem. I have gone through Hoffman and kunje and Axler earlie. I found Hoffman so much time taking it builds topic slowly. But whatever portion I studied from that book till linear transformation it was amazing.I want to know whether I should go through these books again or is there a text which I can go through for second course in linear algebra?

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When I took linear algebra at Berkeley in the late 80's, Bill Jacob taught from his book, which was still in manuscript form. He was quite good, and I would recommend the book. I looked him up recently, and he is now head of the department at UCSB. He is quite accomplished...

Then there is Gilbert Strang's book, Linear Algebra and Its Applications, i think it is called. As the title suggests, it has a decidedly applied feel. I think it's pretty good. Btw, he's a professor at MIT.

There was a popular book by an author named Anton, i believe it was.

As you mentioned, there are quite a few.

Finally, i believe my former advisor Peter Petersen at UCLA has a book on the subject. Though I can't tell you anything about it's focus or approach, it should be pretty good.

Oh, and one last one: P R Halmos wrote a book called Finite Dimensional Vector Spaces which is supposed to be pretty good...

Just to name a few...

Sorry I can't remember for sure if they cover the topics you mentioned; but I have a feeling they are pretty standard.

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  • $\begingroup$ Actually in strang's book he has used matrices. I want to go through a book which describe linear algebra through linear transformation and then discover the properties of matrices. As Hoffman or Axler they have not focused much on matrices..thanks for your suggestions $\endgroup$ – Prakash Nainwal Jul 27 '18 at 7:40
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My favorite Linear Algebra textbook is Katsumi Nomizu's Fundamentals of Linear Algebra. It covers those topics that you are interested in.

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  • $\begingroup$ Why a -1? This answers the question. $\endgroup$ – Paul Jul 27 '18 at 8:13
  • $\begingroup$ @Paul I suppose that this was meant as an attack on me, rather than a criticism os my answer. I say this because at the same time that I got this downvote, I got another one to my answer to this question $\endgroup$ – José Carlos Santos Jul 27 '18 at 8:15
  • $\begingroup$ Life on the internet I suppose. $\endgroup$ – Paul Jul 27 '18 at 8:34
  • $\begingroup$ +1 to compensate idiocy and since the book indeed addresses those topics. $\endgroup$ – Mathematician 42 Jul 27 '18 at 8:53
  • $\begingroup$ @Mathematician42 Thank you. That was a nice gesture. $\endgroup$ – José Carlos Santos Jul 27 '18 at 9:01

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