a while ago i asked about tensor stuff. since then ive made significan progress. Let A and B be vectors with Both Real and complex components

Normal scalar product is AB (the dot between is assumed to be, if its cross iĀ“ll have a little x)

and in tensor you take like

n=d<sub>cz</sub> A<sup>c</sup> B<sup>z</sup>

d<sub>cz</sub> is the kronecker delta (spelled right?)

hope im right this far

but then when it comes to complex vectors the scalar product is called inner product, right? and look like

<A|B> = AB*

where the * after B means it is its complex conjugate.

My question is, how do you write this in tensor form?