Reference request for dual spaces. I am a graduate student of Mathematics.I want to study dual spaces,linear functionals and transpose of a linear operator.But I am lacking a suitable text for that.I have tried Hoffmann Kunze and Friedberg-Insel-Spence but those books lack motivation.I am finding a book that gives motivation for studying dual spaces and also explains the theory nicely.Can someone help me find a suitable text?
 A: There are two possibilities I can think of that you may wish to look at, and see if they suit your taste/learning style. One is Linear Algebra Done Right by Axler, which goes into all the topics you mention, although from memory doesn't go too deep into motivation. I do recall that the topic of dual spaces and functionals is dealt with pretty well. There are also lots of end-of-chapter problems, and solutions are pretty easily found online.
If you are affiliated with a university you can download it for free on the SpringerLink website: https://link.springer.com/book/10.1007/978-3-319-11080-6 (the material on dual spaces begins around p.101.)
Another one is Linear Algebra and Geometry by Kostrikin/Manin, which uses a geometric context to motivate most of the material covered, which is mostly upper-level linear algebra. They cover the topics you mentioned, but its been a while since I looked at it, so I can't recall the quality of the treatment of those topics specifically. However, the book is of very high quality, and I do remember getting a lot out of it. Anyway, take a look!
