The Lectures on Linear Algebra covers fundamental topics designed to build a robust foundation:
Whenever possible, translate the algebra into a geometric sketch.
Because the book is highly concise, reading it requires active participation.
Gelfand treats matrices not as boxes of numbers, but as representatives of linear operators. He is meticulous about the distinction between an operator (a geometric action) and its matrix (a specific coordinate expression).
If you download the PDF and open it, you might be shocked. It is not a "pretty" textbook. There are no color photographs of architectural columns, no biographies of Gauss on the margins, and no QR codes to YouTube videos.
For students, engineers, and mathematicians, yes. The Dover Publications edition is widely accessible and affordable, making the text easily available. A is an excellent tool for quick searching and referencing concepts, but the depth of the material often necessitates active reading with a pen and paper. Tips for Studying Gelfand
