Can A Tensor Multiplied by 0 Produce a Null Tensor?

[tenchotomic]

Mutiplication of a scalar by a 0 gives 0(scalar)

And also one proves in linear vector spaces that a vector(|>) combined with 0 by multiplicative law gives |0> .

Similarly can one prove that multiplication of a tensor of say rank 2,by 0 will produce a null rank 2 tensor.

 

[pessimist]

yes one can.

 

[tenchotomic]

yes one can.

Iam asking for an idea on how to do it?

 

[pmsrw3]

Iam asking for an idea on how to do it?

Well, in my books, a tensor is by definition a multilinear map from a bunch of vector spaces to the reals. The result you want comes right out of the linearity.