The set of invertible $k \times k$ matrices with complex entries is a connected subset of $\Bbb C^{k \times k}$.
102084
How to show path-connectedness of $GL(n,\mathbb{C})$
39334
Non-degenerate bilinear forms and invertible matrices
55493
Showing that the path-connected component of the identity matrix in a subgroup of $GL_n(\Bbb R)$ is a normal subgroup
27474
A square matrix $n \times n$ is an invertible matrix iff the rank of the matrix is $n$.
55230
Dimension of set of commutable matrices
115695
If $X$ is a connected subset of a connected space $M$ then the complement of a component of $M \setminus X$ is connected
154534
consider the following subsets of complex plane
57943
If $G$ is a convex set, prove that $\mathbb{C}\cup\{\infty\}\setminus G$ is connected.
71102
Subfields of $\mathbb{C}$ which are connected with induced topology
44685
Inner product on $C(\mathbb R)$
43503
Bases of complex vector spaces and the axiom of choice
78298
On the nilpotence of the matrix $AB-BA$
48557
Product of connected spaces
26919
Intersection of Connected Sets
134162
What is a basis for the space of $n\times n$ Hermitian matrices?
97781
invertible matrices connected or not
75215
Properties of invertible matrices