Tagged Questions
3
votes
1answer
81 views
Topological properties of symmetric positive definite matrices
Let $S$ be the set of all symmetric positive definite matrices of size $n\times n$. Which of the following statements are true?
(a) $S$ is closed in $\mathbb{M}_n(\mathbb{R})$.
(b) $S$ is ...
2
votes
1answer
53 views
$GL(2,\mathbb{R})$ as a subset of $\mathbb{R}^4$
If we consider $GL(2,\mathbb{R})$ as a topological subspace of $\mathbb{R}^4$ with the usual topology and want to know if it compact or not then if we could show that it was not closed then we would ...
10
votes
2answers
792 views
Topology of matrices
1.Consider the set of all $n×n$ matrices with real entries as the space $\mathbb R^{n^2}$ .
Which of the following sets are compact?
(a) The set of all orthogonal matrices.
(b) The set of all ...
3
votes
1answer
137 views
Which of the following are compact sets?
Which of the following are compact sets?
$\{\operatorname{trace}(A): A \text{ is real orthogonal}\}$
$\{A\in M_n(\mathbb{R}):\text{ eigenvalues $|\lambda|\le 2$}\}$
Well, orthogonal matrices are ...
