# Multiplication by zero

1. Jul 19, 2011

### 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.

2. Jul 19, 2011

### pessimist

yes one can.

3. Jul 19, 2011

### tenchotomic

Iam asking for an idea on how to do it?

4. Jul 19, 2011

### pmsrw3

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.