Show that the set of invertible $n\times n$ matrices with entries in $\mathbb{R}$ is not connected?
46917
How to prove that $GL(n,\mathbb R)$ is not connected subset and open subset of$M_n (\mathbb{R})$
127591
How to prove that the collection of rank-k matrices forms a closed subset of the space of matrices?
102299
Bijection between $\mathbb{R}^n$ and $\mathbb{R}^m$
103665
Product of matrices of different order is not invertible
76498
Does every linearly independent set of n vectors in $R^n$ forms a basis in $R^n$?
109217
Invertibility of the Product of Two Matrices
69497
Show that the set of all $n \times n$ orthogonal matrices, $O(n)$, is a compact subset of $\mbox{GL} (n,\mathbb R)$
107389
Show that the vector space of real functions is not finitely spanned
114271
Why is a matrix invertible if it can be written as the product of elementary matrices?
18145
Diagonalizable matrices with complex values are dense in set of $n\times n$ complex matrices.
74330
$\mathbb{R}^n$ not homeomorphic to open subset of $\mathbb{R}^m$
86749
Prove that any set of vectors $S \subset \mathbb{R}^n$ containing the zero vector cannot be linearly independent
10911
$A \in M_{n}(\mathbb{R})$ has inverse if and only if it's rank is n.
155272
Is a matrix with $1$s in the diagonal and off-diagonal entries with absolute value less than $1$ invertible?
151719
Connected set in $\mathbb{S}^1$
124942
Prove that an upper triangular matrix is invertible if and only if every diagonal entry is non-zero.
150387
Questions about matrix rank, trace, and invertibility