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I find myself regularly looking up common vector identities in index-tensor notation like the following simple examples

$(u\times v)_i = \epsilon_{ijk} u_j v_k$ (in 3-space)

or

$u\cdot v = u_iv_i$

$(MN)_{ij} = M_{ik}N_{kj}$

(with the implied summation over repeated indices - abuse of Einstein notation where the covariant/contravariant distinction is not important)

These are easy to remember, but other - more complex - vector/matrix expressions either require working them out by hand, or hunting them down

Is there a reference available in "cheat sheet" form that lists a good amount of these identities concisely? Something like a table of integrals but for common vector memes written in index notation.

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    You mean like $\epsilon_{ijk} A^j_a u^a A^k_b v^b$? The conversion to Einstein notation can be done just by composing the translation rules and fishing for new indices as needed. Do you mean the conversion back from Einstein notation, or just how you would chain together the translation?2011-10-05

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