Mike Usher
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Registered User
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Mar 25 |
awarded | ● Nice Answer |
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Jan 12 |
comment |
real symmetric matrix has real eigenvalues - elementary proof I'm confused by your (2)...doesn't putting $S=\left(\begin{array}{cc} 0 & 1 \\ 1 & 0\end{array}\right)$ and $z=\left(\begin{array}{c} 1 \\ 0\end{array}\right)$ give a counterexample? The statement that $\langle Sz,z\rangle=0$ isn't enough to imply that $z$ is orthogonal to the range. |
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Jan 11 |
accepted | On the de Rham cohomology of 1-forms in cotangent bundle. |
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Jan 11 |
comment |
On the de Rham cohomology of 1-forms in cotangent bundle. In your example on $S^1$, note that the vertical translation on the cylinder is a symplectic isotopy but is not Hamiltonian (i.e. is not given by the flow of the Hamiltonian vector field of a time-dependent function--its flux is nonzero). So if one is restricting to Hamiltonian flows (as the OP seems to be doing) this example doesn't apply. |
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Jan 11 |
answered | On the de Rham cohomology of 1-forms in cotangent bundle. |
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Dec 26 |
awarded | ● Nice Answer |
