Understanding the Colon Notation:

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In summary, the colon notation, :, can represent a double dot product and can be used in place of the inner product notation, <, >. It is still unclear how this notation is being used in the context of locally integrable functions and distributions.
  • #1
Integrals
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What does the colon notation, :, mean?
 
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  • #2
Integrals said:
What does the colon notation, :, mean when it is inside an integral for weak solutions?
Can you be a bit more precise and descriptive?
 
  • #3
fresh_42 said:
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...
 
  • #4
I haven't seen the first one, and the second one calls for the question, what are you multiplying there?
 
  • #5
fresh_42 said:
I haven't seen the first one, and the second one calls for the question, what are you multiplying there?
Locally integrable functions - where $$\mathbf{x}=(x_1({\cdot}), x_2({\cdot}), x_3(\cdot))$$
 
  • #6
How is this related to distributions?
 
  • #7
Integrals said:
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?
 
  • #8
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##?
 

1. What is colon notation?

Colon notation is a way of representing relationships between objects in a hierarchical structure. It is commonly used in computer science and mathematics to denote parent-child relationships.

2. How is colon notation used?

Colon notation is used to show the relationship between an object and its sub-objects. It is often used in programming languages, such as Python, to access attributes or methods of an object.

3. What does the colon (:) symbol represent in colon notation?

The colon symbol represents the "is a" or "belongs to" relationship between objects. It indicates that the object on the left is the parent or superclass, and the object on the right is the child or subclass.

4. Can colon notation be used for more than two levels of hierarchy?

Yes, colon notation can be used for any number of levels of hierarchy. It can be extended to show relationships between multiple levels of parent and child objects.

5. Are there any other notations that serve a similar purpose to colon notation?

Yes, there are other notations that are used to represent hierarchical relationships, such as dot notation and arrow notation. These notations may vary in syntax and usage, but they all serve the purpose of denoting relationships between objects.

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