Recommended Book after Finite-Dimensional Vector Spaces by Halmos I really like "Finite-Dimensional Vector Spaces" by Paul Halmos (Undergraduate Texts in Mathematics).
Is there any graduate level version of this book (not necessarily by Halmos), i.e. similar subject and style but at a more advanced level?
I am not really interested in the analysis part (e.g. convergence, completeness etc) but rather more interested in the algebraic parts like Eigenvalues, Eigenvectors and Spectral Theorems.
Thanks for any recommendations.
 A: I would advise you to try out Greub's Linear Algebra book. It is a graduate text, and the author is very rigorous in the threatment of the subject.
If you like, you can read the short review that I have written about the book from here.
Edit:
In the last year, I have covered more than half of the book, and asked lots of questions in this site about the material, so if you stuck at some point as I have done, you can check out the posts that I have asked, or directly post a question in here (obviously), I would be happy to answer if I can.
A: Besides Greub's text, here are a few others that appear to fit your objectives . . . 


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*Roman -- Advanced Linear Algebra, 3rd Ed (2008)

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From the preface: 


This book is a thorough introduction to linear algebra, for the graduate or advanced undergraduate student.$\\[10pt]$


*Blyth & Robertson -- Further Linear Algebra (2001)

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From the preface: 


Our title "Further Linear Algebra" suggests already that the reader will be familiar with the basics of this discipline.$\\[10pt]$


*Cooperstein -- Advanced Linear Algebra, 2nd Ed (2015)

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From the preface:


. . . through the choice of various subsets of the chapters, this book can be appropriate for a single upper-division or graduate course in linear algebra, . . .


