# Thread: skew symmetric system problem

1. The following system is skew symmetric in all of its indices:

such that:

I'm asked to prove it has 27 elements (easy since its ), and that 21 of these are zero. The remaining six occur when (p,r,s)=(1,2,3).

How can I go about proving this? Thanks

2.

3. Originally Posted by Nabla
The following system is skew symmetric in all of its indices:

such that:

I'm asked to prove it has 27 elements (easy since its ), and that 21 of these are zero. The remaining six occur when (p,r,s)=(1,2,3).

How can I go about proving this? Thanks
This sounds suspiciously like a homework problem.

You need to do your own homework.

It is actually pretty simple.

4. It's not homework, I'm working through some online notes on tensor calculus and differential geometry, as a personal task (I'm currently on my summer holidays). This is a question from the first section of those notes which introduces index notation.

5. Originally Posted by Nabla
It's not homework, I'm working through some online notes on tensor calculus and differential geometry, as a personal task (I'm currently on my summer holidays). This is a question from the first section of those notes which introduces index notation.
Then the result is very simple to prove. The skew symmetry implies that if you interchange any two indices then the result is the same as multiplying by -1, so if two indices are the same, then the term, being its own negative, must be 0. Therefore the only non-zero terms must be in cases in which the indices p,r,s take on different values and the ony available values are 1,2,3.

6. Thanks. That's actually really simple, I'm annoyed for not figuring it out myself.

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