Does it indicate this?
$L=U$ \ $C=U^TC$
$Q=U$ / $C=UC^{-1}$
Can you please provide any references for these two symbols for matrix computation?
[Update] according to [http://en.wikipedia.org/wiki/Division_(mathematics)#Of_matrices], it seems it means inverse or pseudoinverse.
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The following is the segment I saw in a paper:
The operators mean "division" sort of as they would for numbers. Specifically you can think of as $A \backslash B$ as $A^{-1}B$ and of $ B/ A$ as $B A^{-1}$. But more precisely it is "solution of $A X = B$" and "solution of XA=B" (where "solution" might even have a meaning of approximate solution only).
The fact that once the transpose appears is merely due to the fact that in that case the inverse is the transpose as the matrix is orthognal.
For example in MATLAB $A \backslash b$ means (is the syntax for) "solve $Ax = b$" see http://www.mathworks.fr/help/matlab/ref/mldivide.html
I notice you added some update: yes, that's it basically.