Chapter 19: Problem 2
Show that the special orthogonal group \(S O(n)\), the pseudo-orthogonal groups \(O(p \cdot q)\) and the symplectic group \(S p(n)\) arc all closed subgroups of \(G L(n, \mathbb{R})\). (a) Show that the complex groups \(S L(n, \mathbb{C}), O(n, C), U(n), S U(n)\) are closed subgroups of \(G L(n, C)\) (b) Show that the unitary groups \(U(n)\) and \(S U(n)\) are compact groups.
Short Answer
Step by step solution
Key Concepts
These are the key concepts you need to understand to accurately answer the question.