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Hey,

I've got to show [tex] \nabla \vec{V} [/tex] is a (1 1) tensor with components [tex] V^\alpha{}_{;\beta} [/tex]. Do I need to show (a) that it is a multilinear map or (b) that the components transform tensorially? I don't know how to do it using method (a) and method (b) involves chrictoffel symbols and how they transform and it doesn't lool pretty. Any help?

I've got to show [tex] \nabla \vec{V} [/tex] is a (1 1) tensor with components [tex] V^\alpha{}_{;\beta} [/tex]. Do I need to show (a) that it is a multilinear map or (b) that the components transform tensorially? I don't know how to do it using method (a) and method (b) involves chrictoffel symbols and how they transform and it doesn't lool pretty. Any help?

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