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It provides an introduction to Lie groups, Lie algebras and their representations as well as introduces some directions of current research for graduate students who have little specialized knowledge in representation theory.

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Lectures on Linear Algebra I. Part IV covers some advanced material on infinite-dimensional representations of non-compact groups such as the orbit method, minimal representations and dual pair correspondences, which introduces some directions of the current research in representation theory.

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## Gelfand – Lectures on Linear Algebra

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They then cover eigenvalues, eigenvectors, singular value decomposition, Jordan decomposition including a proofquadratic forms, and Kronecker and Hadamard products.