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?
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.
My favorite Linear Algebra textbook is Katsumi Nomizu's Fundamentals of Linear Algebra. It covers those topics that you are interested in.