# A Meaning of Slot-Naming Index Notation (tensor conversion)

#### heptacle

I'm studying the component representation of tensor algebra alone.
There is a exercise question but I cannot solve it, cannot deduce answer from the text. (text is concise, I think it assumes a bit of familiarity with the knowledge)

(a) Convert the following expressions and equations into geometric, index-free notation:
AαBγβ ;
AαBγβ ;
Sαβγ=Sγβα ;
AαBβ=AαBβgαβ

In this problem, I can't see any difference between first two expressions except for the index position, and my only solution for the expression of index position is using metric tensor g, which I think is included in slot-naming notation. Is "index-free" notation can express the difference?
Other expressions are similarly confusing for me.

(b) Convert T(_,S(R(C,_),_),_) into slot-naming index notation.

I think this notation would be not so universal notation. These problem are from http://www.pmaweb.caltech.edu/Courses/ph136/yr2012/1202.1.K.pdf (Ex 2.7)
and the help of anyone who is familiar with the notation would be appreciated.

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#### PF_Help_Bot

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"Meaning of Slot-Naming Index Notation (tensor conversion)"

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