query: How to prove 2x2 rotation matrix is a manifold
positive_passages.docid: 156245
positive_passages.text: What does it mean for the group of rotation matrices to have a "manifold structure"
negative_passages.docid: 151228
negative_passages.text: What are the requirements for a rotation matrix?
negative_passages.docid: 13964
negative_passages.text: Manifold of Density Matrices
negative_passages.docid: 135126
negative_passages.text: Proving that the quotient manifold is orientable if and only if the group action is orientation-preserving
negative_passages.docid: 134362
negative_passages.text: Rotation of group of rigid motions of cube is isomorphic to $S_{4}$
negative_passages.docid: 90092
negative_passages.text: Showing that $\bar{\mathbb{B}}^n$ is a manifold with boundary (Lee ITM Probelm 3-4)
negative_passages.docid: 109643
negative_passages.text: Prove that every isometry on $\mathbb{R}^2$ is bijective
negative_passages.docid: 102418
negative_passages.text: Rotations preserve cross products?
negative_passages.docid: 18921
negative_passages.text: Linear Transformations: Proving 1 dimensional subspace goes to 1 dimensional
negative_passages.docid: 135108
negative_passages.text: Why doesn't $ds^2 = 0$ imply two distinct points $p$ and $p'$ on a manifold are the same point?
negative_passages.docid: 84419
negative_passages.text: Product of manifolds & orientability
negative_passages.docid: 90365
negative_passages.text: Riemannian Manifolds with $n(n+1)/2$ dimensional symmetry group
negative_passages.docid: 117175
negative_passages.text: Proof that the 2-norm of orthogonal transformation of a matrix is invariant
negative_passages.docid: 121909
negative_passages.text: Are matrices and second rank tensors the same thing?
negative_passages.docid: 80100
negative_passages.text: Boundary of product manifolds such as $S^2 \times \mathbb R$
negative_passages.docid: 138025
negative_passages.text: How to show the solution of $\dot{x} = Ax $ is an invariant subspace?
negative_passages.docid: 58595
negative_passages.text: Existence of a G-invariant matrix