Tensor

[john_mawlai]

Hi, Can anyone help me with this:

Let B^qn_r be an arbitrary tensor.

[Here q n are contravariant indices and r is covariant index.]

 

Suppose we have a quantity X(p, q, r) such that X(p, q, r) B^qn_r = 0.

Is X(p, q, r) identically zero?

Thanks a lot in advance.

 

john_mawlai.

[Bignose]

john,

 

this forum doesn't answer homework questions directly (and, this looks an awful lot like homework), so the 1st question is what do you think and why?

[ajb]

I am not sure what [math]X(p,q,r)[/math] is. Is it a scalar?

 

Anyway, a little clue might be that if all components of a tensor are zero in one coordinate system, then they are all zero in any coordinate system.

Edited August 4, 2010 by ajb