Let a be a vector, then $a\times b=[a]_{\times}b$, what is $[a]_{\times}$?

If a=[a1,a2,a3]^T, then

$[a]_{\times}=$

[0 -a3 a2]
[a3 0 -a1]
[-a2 a1 0]

You can check it using the definition of cross product, see http://en.wikipedia.org/wiki/Cross_product.