Lie groups: Show $L_y \circ x_t = x_t \circ L_y$ where $x_t$ is the flow of a left invariant differentiable vector field
98800
Do local flows of left-invariant vector fields satisfy $\Phi_X^t\circ L_x=L_x\circ \Phi_X^t$?
138025
How to show the solution of $\dot{x} = Ax $ is an invariant subspace?
61013
Diffeomorphism between the Grassmannian manifolds $\mathbf{Gr}(n,k)$ and $\mathbf{Gr}(n,n-k)$.
66283
Let V be a vector space. If every subspace of V is T-invariant, prove that there exist a scalar multiple c such that T=c1v
146730
The adjoint of left exterior multiplication by $\xi$ for hodge star operator
73406
Prove that $E_{\lambda}(T)=E_{\lambda^{-1}}(T^{-1})$ if $T$ is an invertible linear operator on a finite dimensional vector space $V$
118049
Show that $\mathbb{R}^{\mathbb{R}} = U_{e} \oplus U_{o}$
144097
eigenvalues and eigenvectors of $vv^T$
116750
On surjectivity of exponential map for Lie groups
105293
Proof of the second symmetric derivative
92033
Prove that $g$ is a submanifold: $g (t,u,v) = (t^2,u^2,v^2,\sqrt{2}uv, \sqrt{2}tv,\sqrt{2}tu)$
28935
Lagrangian of the Euler equations
13644
Is the change in the Lagrangian always a total derivative for symmetry transformations of the action?
128921
Why define $(\nabla^2F)(X,Y)=\nabla_X(\nabla_YF)-(\nabla_{\nabla_XY}F)$?
39094
Lie bracket of vector fields on $\Bbb R^{n}$
61593
Adjoint map is Lie homomorphism
118996
Prove that $T$ is an orthogonal projection