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## Main Question or Discussion Point

I know the arrow -> means a map.

For example,
defines a linear map. But I cannot figure out what does a X mean?

I know that above denote a inner product map. whatever is on the left of the : is defined by whatever is on the right. but what is the x symbol? What is the correct way to read it? Is there a basic book that can tell me more about these symbols?

For example,

I know that above denote a inner product map. whatever is on the left of the : is defined by whatever is on the right. but what is the x symbol? What is the correct way to read it? Is there a basic book that can tell me more about these symbols?