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Memo: skew-symmetric matrix associating a vector

01/11/2011

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.

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