Gelfand begins by defining the abstract concept of a vector space over a field. Concepts of linear dependence and independence. Dimension and basis of a space. Properties of subspaces and intersections. 2. Linear Transformations and Matrices
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If you are determined to find a free, high-quality scan, search for the Russian title "Лекции по линейной алгебре" or the exact ISBN of the Dover edition: 978-0486660824 . Many university math departments host copies for course reserves. Gelfand begins by defining the abstract concept of