| Source | Format | Cost | |--------|--------|------| | Dover Publications (direct) | Print | ~$15 | | Amazon | Print, Kindle | ~$15 | | Google Books (snippet view only) | Preview | Free to search | | Internet Archive (controlled digital lending) | PDF scan (1‑hour loan) | Free (with account) | | Many university libraries (via ProQuest Ebook Central or similar) | PDF chapter downloads | Free for students |
➡ Internet Archive link (check if still available for borrowing):
archive.org/details/lecturesonlinear0000gelf
One of Gelfand’s greatest gifts is his constant eye on the horizon: functional analysis. He doesn’t treat linear algebra as a closed subject. Instead, he presents finite-dimensional vector spaces as a warm-up for the infinite-dimensional spaces found in quantum mechanics (Hilbert spaces). This is why physicists adore this book. gelfand lectures on linear algebra pdf
Unlike American textbooks that spend 200 pages on 2D and 3D vectors, Gelfand moves immediately to ( n )-dimensional space. He introduces the concept of a field (real and complex numbers) not as an obstacle, but as a tool. He defines vectors as ordered ( n )-tuples and immediately discusses linear dependence.
Key Insight: He proves that in an ( n )-dimensional space, no more than ( n ) vectors can be linearly independent. This is not a rule; it is a logical consequence of the definition. | Source | Format | Cost | |--------|--------|------|
Lectures on Linear Algebra was originally published by Interscience Publishers (later Wiley) in the 1960s. Today, it is available as a Dover Publications edition (ISBN 978-0486660824). Dover books are notoriously affordable (often $10–$15 new).
However, because the copyright is over 50 years old in some jurisdictions (and still active in others), free PDFs floating on university servers or personal websites exist, but they are frequently out of date, scanned poorly, or missing pages. This is why physicists adore this book
Most modern textbooks bury determinants in the middle of the course. Gelfand introduces them early, but not for computation. Instead, he uses determinants to discuss the very possibility of solving linear systems, leading naturally to Cramer’s Rule as a theoretical tool, not a practical nightmare.