Customer Reviews

Lectures on linear algebra

5 star:		(4)
4 star:		(1)
3 star:		(1)
2 star:		(0)
1 star:		(0)

 

 

The professor who recommended this book made the comment that every time you re-read it, you notice something else that you missed the last time you read it. This is absolutely true.

I must say, the first time I picked up this book, I did not like it. The notation was not what I was used to, and the book dives right in, assuming a lot of background (matrices, determinants, etc.) but covering material which many people find boring (bases, etc.). However, when you read deeper, there's a lot here. Once you get past the ugly notation, the proofs are extraordinarily clear. And in spite of the books small size, there is a remarkable amount of motivation and discussion.

Like the other reviewer said, this is not a book to learn linear algebra from for the first time: this is an advanced book that is useful for graduate students who have already had a linear algebra course and who want to learn more topics, or understand topics on a deeper level.

This is an excellent book; the bottom line is that it's so cheap that there's no excuse NOT to buy it.

This is a good book if all you need is a condenced reference on theorems and proofs and it assumes that you go for practice (and instruction) elsewhere. If you are trying to actually learn linear algebra (especially on your own and especially if you want to learn how to solve practical problems) get one of Gilbert Strang's books and watch his videolectures at MIT web site. Another thing that I dislike about the Gelfand's book is that it puts too much emphasis on index notation - instead of matrix notation wich is natural for linear algebra, almost all formulas and theorems are presented at very low level using expressions consisting of variables with multiple indices. Naturally it gets very messy and hard to follow at times. This doesn't present any more information than equivalent matrix notation but introduces unnecceccary complexity and makes things that are really easy to understand very confusing.

I can only strongly recommend this somewhat forgotten textbook to anyone who needs a basic but otherwise thorough exposition to linear algebra. It conflates rigor, examples, and exercises very nicely, although in a very economic manner. Its coordinate-oriented presentation may not appeal to the mathematician in search of ultimate generality, but it is ideal for the physics and engineering-minded person. It is unfortunate that nowadays so many S&E students become first aquainted with rings of polynomials than with rotation matrices! Do not get me wrong, though: the book contains real math inside, but in the best Russian textbook presentation tradition.

The bilinear (quadratic like) form is related to the inner product in this text: two things that are almost entirely left out in many American linear algebra texts. The text is a translation from Russian and
is somewhat difficult with the axiomatic development form used.
Explanations, examples and problems aren't a real part of this method of presentation, so the resulting text is more like a graduate text
than the second year texts of American Linear algebra.
The price is right for real students of algebra.

This is the best treatment of linear algebra that has been published. It starts with n-Dimenaional linear spaces and ends with an introduction to tensors. An excellent description of dual spaces is consicely presented. NO INDEX!

Lucid and clear notation , complete explanations . This books was first published in
1937 but until now it remains best text book in the field .