Several answers have been posted here, but here, my main aim is not to post just answer, but to catch attention of learners of Linear algebra, of graduates, who want more to know on linear algebra.
A modern Linear Algebra which I like much is the book by Charles Curtis. To mention few features of this book, not with style of writing, but with content, are following:
(0) Many basic concepts of Linear algebra are motivated with simple examples in algebra as well as school geometry; for, one can have overlook in exercises of all chapters.
(1) In my undergraduate, I was searching for different books to understand Jordan Canonical Forms, but I found no books in my Library, except little exposition in H&K. But long time after completion of graduation, I came across this book, and found its beautiful exposition on Jordan theory.
(2) If you search for Adjoint transformation in google books, mostly you will see that it is introduced in chapter with title Inner product spaces. But, this concept of adjoint transformation do not requires space to be inner product space, and this is the only book I saw explained it in this general setting, so as soon as we have a linear transformation between "vector spaces", we can quickly go to "what is adjoint of it", without considering whether what inner product is there.
(3) When I came across looking for Jordan decomposition of linear operators (=semisimple+nilpotent), then, much of the tools to prove it are hidden in primary decomposition theorem or Jordan canonical forms; this is the only book I saw which beautifully explains this decomposition. I didn't get this theorem even in books of Algebra or Linear Algebra by famous algebraists.
(4) The book first geometrically explains concept of determinant, which I rarely find in other books.
(5) Finally, when reading this book of Curtis, I found his language much beautiful, elegant, and not creating fear of any simple or difficult concept, which shows that the subject could be easily learned by anyone just with this book.
One can even find a different elegant exposition to other important concept of linear algebra in this book (principal axis theorem, symmetry); but I couldn't not mention it fully, instead leave the reader to see at least once the book.
A point to mention here: I was searching reviews before writing these points of the book, but I didn't get its review in MAA; so I tried to write my experience with this book, which kept me enjoying the subject any time.