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Notes on Optimization on Stiefel Manifolds - Yale University
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LECTURE 2: SMOOTH MANIFOLDS - USTC
WebLet : be a smooth map between smooth manifolds and .Then there is an associated linear map from the space of 1-forms on (the linear space of sections of the cotangent bundle) to the space of 1-forms on .This linear map is known as the pullback (by ), and is frequently denoted by .More generally, any covariant tensor field – in particular any differential form … Web2 LECTURE 2: SMOOTH MANIFOLDS of charts. In other words, if both ’and are chart maps near a point, we want the maps f ’ 1 and f 1 to be simultaneously smooth or non-smooth. This amounts to require ’ 1 to be smooth. (Note: even though f ’ 1and f are both smooth, we still want the map ’ 1 1to be smooth so that the di erentials of f ’ and f are nicely http://support.ricoh.com/bb_v1oi/pub_e/oi/0001061/0001061869/VF20160408/F20160408_pt.pdf roadwish 携帯ポンプ