Matrix Groups

and symplectic groups. The relation of complex to real matrix groups is also studied. Along the way we discuss various algebraic, analytic and topological notions including norms, metric spaces, compactness and continuous group actions.

Matrix Groups

Matrix Groups

This book offers a first taste of the theory of Lie groups, focusing mainly on matrix groups: closed subgroups of real and complex general linear groups. The first part studies examples and describes classical families of simply connected compact groups. The second section introduces the idea of a lie group and explores the associated notion of a homogeneous space using orbits of smooth actions. The emphasis throughout is on accessibility.

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