گروه های ماتریسی و مقدمه ای بر نظریه گروه لی

This work provides a first taste of the theory of Lie groups accessible to adadvanced mathematics undergraduates and beginning graduate students, providing an appetiser for a more substantial further course. Although the formal prerequisites are kept as low level as possible, the subject matter is sophisticated and contains many of the key themes of the fully developed theory. We concentrate on matrix groups, i.e., closed subgroups of real and complex general linear groups. One of the results proved is that every matrix group is in fact a Lie group, the proof following that in the expository paper of Howe [12].