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**1. The problem statement, all variables and given/known data**

I have been working on defining the transpose in a tensorial view using the kroneck delta tensor.

**2. Relevant equations**

I will use tensor notation

**3. The attempt at a solution**

Let T

_{jk}be a 2

^{nd}level tensor:

(T

_{jk})

^{TP}= T

_{kj}

My first attempt is:

δ

_{jk}T

_{jk}δ

_{kj}= T

_{kj}

However if tensor components are commutable by nature the above expression can be

δ

_{jk}δ

_{kj}T

_{jk}= δ

_{jk}T

_{kk}

the latter expression becoming ambigious, I can replace either k and acquire:

δ

_{jk}T

_{jj}= T

_{jk}

or

δ

_{jk}T_{jj}= T_{kj}