Doubt on proof showing matrices of certain rank form a submanifold.
137093
What is the codimension of matrices of rank $r$ as a manifold?
127799
Eigenvalues of symmetric matrices are real without (!) complex numbers
37162
Prove that matrices have equal rank.
156877
Rank-one perturbation proof
119435
Rank of the difference of matrices
125569
Prove that the eigenvalues of a real symmetric matrix are real
24691
Relation bewteen Hessian Matrix and Curvature
75104
Existence of some type matrix
19649
A question about the proof of "a symmetric matrix has real eigenvalues".
56312
Why can this product of rectangular matrices not be the identity matrix?
4205
Is adjoint of singular matrix singular? What would be its rank?
157742
Prove that $U(n)$ is a manifold
152932
Proof: $\det\pmatrix{\langle v_i , v_j \rangle}\neq0$ $\iff \{v_1,\dots,v_n\}~\text{l.i.}$
39334
Non-degenerate bilinear forms and invertible matrices
89649
Linear Algebra munkres analysis on manifolds question.
121253
Prove that any complex matrix can be expressed in term of Hermitian and anti-Hermitian matrices
133449
A proof that an orthogonal matrix with a determinant 1 is a rotation matrix