This is way too vague. What are aαβ, xα and yβ ? For example, in xα is α a superscript or is it x to the α-th power ? Please provide a fuller description.
Thank you.
Here is what I think your post means: you are given a bilinear form in Einstein notation. In my preferred notation it looks like this: S(x,y)=xTAy=∑i,jxiaijyj and condition S(x,x)=∑i,jxiaijxj=0. Then you need to show that aij=−aji, i.e., that A is "skew-symmetric".
Can you see that this equivalent to equation S(x,y)=−S(y,x)? The latter can be proven by looking at S(u+v,u+v).
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