# Double dot product vs double inner product

Anything involving tensors has 47 different names and notations, and I am having trouble getting any consistency out of it.

This document (http://www.polymerprocessing.com/notes/root92a.pdf) clearly ascribes to the colon symbol (as "double dot product"):

$\mathbf{T}:\mathbf{U}=T_{ij} U_{ji}$

while this document (http://www.foamcfd.org/Nabla/guides/ProgrammersGuidese3.html) clearly ascribes to the colon symbol (as "double inner product"):

$\mathbf{T}:\mathbf{U}=T_{ij} U_{ij}$

Same symbol, two different definitions. To make matters worse, my textbook has:

$\mathbf{\epsilon}:\mathbf{T}$

where $\epsilon$ is the Levi-Civita symbol $\epsilon_{ijk}$ so who knows what that expression is supposed to represent.

Sorry for the rant/crankiness, but it's late, and I'm trying to study for a test which is apparently full of contradictions. Any help is greatly appreciated.

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What course is this for? I've never heard of these operations before. (Sorry, I know it's frustrating. There are a billion notations out there.) – Jesse Madnick Apr 2 '13 at 5:43
It's for a graduate transport processes course (for chemical engineering). – Nick Apr 2 '13 at 5:49