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I am reading Steven Roman's book, Advanced Linear Algebra and am currently focussed on Chapter 1: Vector Spaces ... ...
I need help/clarification with respect to a notational issue regarding Roman's definition of the direct product and external direct sum of a family of vector spaces ... ...
Roman defines the direct product and the external direct sum of a family of vector spaces on page 41 as follows:View attachment 5088In the above definitions Roman does not define $$K$$ ... nor as far as I can see, does he define it earlier in the book ...
... ... so my question is ... ... what is the exact nature of the set $$K$$ ... can it be any set? ... looks like it should be something like $$\mathbb{N}$$ ... but maybe it can be more general ...
Can someone please clarify this issue for me?
Hope someone can help ... help will be appreciated ...
Peter
I need help/clarification with respect to a notational issue regarding Roman's definition of the direct product and external direct sum of a family of vector spaces ... ...
Roman defines the direct product and the external direct sum of a family of vector spaces on page 41 as follows:View attachment 5088In the above definitions Roman does not define $$K$$ ... nor as far as I can see, does he define it earlier in the book ...
... ... so my question is ... ... what is the exact nature of the set $$K$$ ... can it be any set? ... looks like it should be something like $$\mathbb{N}$$ ... but maybe it can be more general ...
Can someone please clarify this issue for me?
Hope someone can help ... help will be appreciated ...
Peter