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What does the colon notation, :, mean?
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Can you be a bit more precise and descriptive?Integrals said:What does the colon notation, :, mean when it is inside an integral for weak solutions?
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 said:Can you be a bit more precise and descriptive?
Locally integrable functions - where $$\mathbf{x}=(x_1({\cdot}), x_2({\cdot}), x_3(\cdot))$$fresh_42 said:I haven't seen the first one, and the second one calls for the question, what are you multiplying there?
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?Integrals said:Locally integrable functions - where $$\mathbf{x}=(x_1({\cdot}), x_2({\cdot}), x_3(\cdot))$$
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.
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.
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.
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.
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.