(a) Prove that the set of all (M) tensors for fixed M, N forms a vector space. (You must define addition of such tensors and their multiplication by numbers.) (b) Prove that a basis for this space is the set {ea Dēß. Dey & w¹ ã' ... wª). ! © M vectors N one-forms (You will have to define the outer product of more than two one-forms.)

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