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Rating: 
Summary: Small introduction to the multilineal algebra
Review: This book is an elementary introduction to the linear Algebra and Tensors. It restricts their study to three dimensions and orthogonal tensors. Their presentation is compact and doesn't introduce a concept that won't be used with posterity in the book. It doesn't follow the limits of a treaty of the lineal algebra, but rather it centers the study of this matter avoiding to enter in messes that are solved in texts more rigorous. You won't find in this text a systematic treatment and complete of the systems of equations lineals, determinants , canonical forms, Etc., but you will be with a very good general concept of the linear algebra along the whole course. Their reading is easy, very didactic, its sections are highly organized and each one of them has a clear objective: no section is unaware to the rest of the book. To read this book you don't need anything. Scarcely you needed something of calculus, and that to understand some examples and does it. If you don't understand in this book the rudiments of the tensors, I believe that you won't understand it in any other one. The book also is full with illustrative examples and problems whose solution will found at the end of the book. This book is a small introduction to the multilineal algebra .
Rating: 
Summary: A decent book with lots of exercises
Review: 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).
Rating:
Summary: A decent book with lots of exercises
Review: 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).
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