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Hello all.

Most modern treatments of the tensor product use equivalence classes to define a quotient space in order to define the tensor product. However in Tensor Analysis on Manifolds, Bishop and Goldberg are much less complicated. I have attached a near word for word copy of their definition.

Why is their's so simple. Why do the other treatments approach it using a more complicated method. Is it just more rigorous.

Matheinste.

Most modern treatments of the tensor product use equivalence classes to define a quotient space in order to define the tensor product. However in Tensor Analysis on Manifolds, Bishop and Goldberg are much less complicated. I have attached a near word for word copy of their definition.

Why is their's so simple. Why do the other treatments approach it using a more complicated method. Is it just more rigorous.

Matheinste.