This is why the PDF is so sought after. It is a "mathematical shock therapy" that condenses a semester of pure thinking into a weekend of reading.
While there is no single document officially titled "Gelfand Lectures on Linear Algebra" (in the same way there are published lecture series by other authors), you are most likely looking for the classic textbook by Israel M. Gelfand . gelfand lectures on linear algebra pdf
Despite being first published decades ago, the book remains a staple for serious students and researchers. Its brevity—often under 200 pages—is not a sign of simplicity but of extreme density. Every sentence is chosen with care, intended to lead the reader toward a "profound understanding" of the subject's elegance. This is why the PDF is so sought after
: Essential for understanding dual spaces and geometry. Gelfand
One of Gelfand’s greatest gifts is his constant eye on the horizon: . 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.
: Covers Euclidean spaces, orthogonal bases, and bilinear/quadratic forms.