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.