Real and Complex Matrix Groups
Throughout, k will denote a (commutative) field. Most of the time we will be interested in the cases of the fields k = ℝ (the real numbers) and k = ℂ (the complex numbers), however the general framework of this chapter is applicable to more general fields equipped with suitable norms in place of the absolute value. Indeed, as we will see in Chapter 4, much of it even applies to the case of a general normed division algebra or skew field, with the quaternions providing the most important non-commutative example.
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