Prove that orthogonal n x n matrices form a $C^1$ surface of dimension n(n-1)/2 in $\mathbb{R^n}^2$
62950
Use implicit function theorem to show $O(n)$ is a manifold
34700
Proving that the matrix exponential map is surjective onto the general linear group
6960
Necessary and sufficient condition for the matrix $A = I - 2 x x^t$ to be orthogonal
56433
Volume form on $(n-1)$-sphere $S^{n-1}$
37060
The Parallelogram Identity for an inner product space
37953
Primary Decomposition of $\mathbb{R^n}$ under T
26801
Show that orthogonal matrices are diagonalizable
141015
Proof of orthogonal matrix
154628
What should we understand from the definition of orthogonality in inner product spaces other than $\mathbb R^n$?
84522
A better proof for $\det(P) = \pm1$ if $P$ is an orthogonal matrix
59477
Density of orthogonal matrices with rational coefficients
34886
Transvection matrices generate $ \operatorname{SL}_n(\mathbb{R}) $
27629
How to prove that $S^{2n+1}/S^1$ is homeomorphic to $\mathbb CP^n$ under a given identification
62303
For $V$ vector space of dimension $n$ under $\mathbb C$ and $T: V \to V $ linear transformation , show $V= \ker T^n \oplus $ Im $T^n$
146847
Given a square matrix A of order n, prove $\operatorname{rank}(A^n) = \operatorname{rank}(A^{n+1})$
127591
How to prove that the collection of rank-k matrices forms a closed subset of the space of matrices?
137093
What is the codimension of matrices of rank $r$ as a manifold?