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cianfa72
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Lie group parametrization as manifold
Hi,
consider the set of the following parametrized matrices
They are member of the group (indeed their determinant is 1). The group itself is homemorphic to a quadric in .
I believe the above parametrization is just a chart for the group as manifold. It makes sense only for and this condition yields an open subset in . On this open set the map is bijective.
That means the are matrices of that cannot be parametrized by the above map (i.e. matrices with the element in the first row/column equal 0).
My question is: the fact that the above parametrization does not cover entirely the group manifold does not rule out in principle that as manifold might be homeomorphic with . Thanks.
consider the set of the following parametrized matrices
They are member of the group
I believe the above parametrization is just a chart for the group as manifold. It makes sense only for
That means the are matrices of
My question is: the fact that the above parametrization does not cover entirely the group manifold does not rule out in principle that
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