which books do you advise with to study linear algebra ?
I haven't read a whole lot of it, but I like what I've read of Lang's Intro to Linear Algebra.
Personally learned a lot from Hoffman and Kunze' Linear Algebra. But it takes close reading, and is probably not great as a supplemental book to a course because it would require too much attention. Basically it might be more advanced than what you are looking for. Are you an engineering student or a math student who is a beginner at linear algebra?
Also, the top negative comment on Amazon is pretty fair in its criticism.
My class is using "Linear Algebra with Applications" by Gareth Williams, 8ed. It reads pretty easily, but at around $200 you might be better off with earlier editions.
The author outlines the changes made between this edition and the 7th in the preface:
i have two linear algebra books
one is basic computation, more geared towards engineers since its also a differential equations book
its differential equations and linear algebra by stephen w. goode and scott a. annin
not much of a fan of the book, but for what its aimed for i'd say it does a fairly good job, and could definitely be used as an intro book
the other one is linear algebra by friedberg, insel, and spence second edition
more on the pure mathematics side with some cool applications to economics and special relativity. i found the second edition for 5 bucks online but the newest edition is the 4th edition. its definitely not an intro book to the subject, but i dont think its too difficult to learn the subject from it either, look for the second edition if you'd like. the first book also seems to refer readers to this book a lot for some of the more advanced proofs.
a lot of people also seem to like axlers book, linear algebra done right, you can check out a chapter or two on axlers, one of the chapters you can preview for free is on inner product spaces, not sure if this is considered an intro book however
I highly recommend Intro To Linear Algebra by Gilbert Strang. The book is mostly focused on application and using Linear Algebra as a workhorse. It forces you to think more on the geometric level and form a better understanding about where these ideas may come from.
If you want a book settled in high rigor with strict proofs and abstract, this is probably not the book for you, but if you want a book that is challenging for a beginner, well thought out, and shows you the power behind linear algebra, then I recommend this book.
I also like what I've read of Friedberg. My class is using Hubbard & Hubbard's Vector Calculus, Linear Algebra, and Differential Forms. It is a great book, but I kind of feel like they present linear algebra subjects in an odd order...
Apostol's Calculus also contains a lot of linear algebra, which I think is a good supplement to a course. If I'm not mistaken, that is what Caltech uses for their linear algebra course. Someone published the linear algebra material from Apostol's calculus as a standalone text, as well.
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