Meaning of the colon (:) symbol in mathematics

Asked Sep 16 '22 at 12:56

Active Sep 16 '22 at 17:51

Viewed 348 times

I've tried to search for the meaning of the colon symbol in the context shown below and can't find an answer. I don't think "such that" makes sense in the formulation below so I'm not sure how to read it. Hoping someone here can help. Thank you.

$$\min_\Gamma\int_{D(\Gamma)}\frac{1}2\nabla y:\nabla y \space dx$$

Equation

edited Sep 16 '22 at 17:51

RobPratt

50,938

asked Sep 16 '22 at 12:56

digits

4

Where did the image come from? What neighboring topics are being discussed? Context is needed. – JMoravitz Sep 16 '22 at 12:58
Thank you for your response. The image is from this paper https://onlinelibrary.wiley.com/doi/10.1002/pamm.202100261 on flow optimization. – digits Sep 16 '22 at 13:01
It has to do with heat and enenrgy. That colon can only be yet another version of the dot product of vectors. Here the two gradients. – Kurt G. Sep 16 '22 at 13:15
That makes sense. Thank you very much! – digits Sep 16 '22 at 13:26
4

I think it's another symbol for this. In the paper $y$ is a vector so $\nabla y$ s a square matrix, so in Einstein notation $\nabla y:\nabla y=\partial_iy_j\partial_iy_j$. – J.G. Sep 16 '22 at 13:33

Meaning of the colon (:) symbol in mathematics

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