An Introduction to Linear Algebra and Tensors, Revised Edition

A very good book for students and professionals alike, who want to strengthen their knowledge of linear algebra and tensors.

it is a concise book.

This book is not the best linear algebra book I've come across, but there are a lot of good things about it. The proofs are all very clear, and there are lots and lots and lots of good exercises. Something I see with a lot of math books on the same topic is that they often have a lot of exercises in common-not usually exactly the same, but difering only by a few numbers or words. But many of the exercises in this book, particularly in the early chapters on dimension, cross product, and dot product, I have not seen in any other book. The one thing about this book is that there really is not a huge amount of non-exercise text-though what there is is well-written. So maybe this would work best as a supplement to another book. One thing that can be said about that book is that, in the division of linear algebra books into computational or abstract algebra books, this book is somewhere in the middle. It starts with the axioms of a vector space, but most of the text concerns only 3-dimensional euclidean geometry-though many(but not all!) of the proofs carry over to higher dimensions without change. Also, the inclusion of so much material on the cross product-which is really useful only in applications to physics(as far as I know), not in abstract mathematics, is another unique feature of this book. Now, this book does not contain things like Gaussian elimination, but it is still not all that abstract, compared to many other books, at least. Also, this book is very short. It covers all the basics, but simply ignores some topics such as tensor products(necessary to a good treatment of tensor products, not messy and index-laden like the one here), exterior products, Jordan normal form, as well as much about what happens if the base field isn't R-in particular, anything about Hermitian or unitary matrices(Unless my memory has failed me-I don't have the book at hand to be sure these things were never mentioned, but am pretty sure).

I wouldn't really title it an introduction book if there are no complete explanations or concepts that must be covered before to understand. We must know about topics such as sets, vectors, differentiation, and such things to fully understand but it is a good book with enough content and practice problems and you will be able to learn new things that would be hard to find on the internet

Excellent introduction to the theory of Cartesian tensors. The presentation of tensors as invariant multilinear forms, leading in a natural way to the transformation formulas and thus motivating them, is worked out very clearly. Unlike many other books, tensors are not simply characterized as multiply indexed quantities that obey certain laws of transformation, thus greatly promoting a deeper understanding. Another plus are many problems, some of them with solutions.

Das Buch ist aus meiner Sicht für Anfänger eher schwer verständlich zu lesen. Kaum Erkärungen, warum (insbesondere bei Tensoren) die eine oder eine andere Definition motiviert sind. Die offensichtlich zumindest teilweise eingescannten Formeln sind auf meinem iPAD schlecht lesbar. Unter dem Strich: leider kein "must have"!