A Weak solutions

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What does the colon notation, :, mean?
 
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Can you be a bit more precise and descriptive?
Apologies for the confusion, is it correct to say that $$\mathbf{x}\otimes\mathbf{x}:y$$ is equivalent notation for $$\langle\mathbf{x}\otimes\mathbf{x}, y\rangle$$ where the latter denotes the inner product. Perhaps, this question was more elementary than I had meant...
 

fresh_42

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I haven't seen the first one, and the second one calls for the question, what are you multiplying there?
 
I haven't seen the first one, and the second one calls for the question, what are you multiplying there?
Locally integrable functions - where $$\mathbf{x}=(x_1({\cdot}), x_2({\cdot}), x_3(\cdot))$$
 

WWGD

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How is this related to distributions?
 

fresh_42

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Locally integrable functions - where $$\mathbf{x}=(x_1({\cdot}), x_2({\cdot}), x_3(\cdot))$$
If I build the ##\mathbf{x} \otimes \mathbf{x}## from this, I get a rank one ##3\times 3## matrix. How can this be multiplied by an ##y## via an inner product, wherever this is from?
 
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The colon can signify a double dot product (see the wikipedia page on Dyadics). It is still ambiguous what is going on here. What is ##y##?
 

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