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Lie Groups, Physics, and Geometry by Robert Gilmore

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3

Matrix groups

 

 

Almost all Lie groups encountered in the physical sciences are matrix groups. In this chapter we describe most of the matrix groups that are typically encountered. These include the general linear groups GL(n; images) of nonsingular n × n matrices over the fields images of real numbers, complex numbers, and quaternions, and various of their subgroups obtained by imposing linear, bilinear and quadratic, and n-linear constraints on these matrix groups.

3.1 Preliminaries

It is first useful to state a simple theorem.

Definition   A subgroup ...

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