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Is it just that $\mathbb K$ is the Skalarraum of $\mathbb K^{m \times n}$, or does it have other applications also?

From a Google search it would seem so, but I'd like to make sure, as none of the pages gives a definition/explanation.

And what would be a more commonly used synonym?

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  • $\begingroup$ The German Raum is the equivalent of the English room. $\endgroup$
    – Lucian
    Nov 3, 2015 at 10:16
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    $\begingroup$ @Lucian, most probably it's space in this context. $\endgroup$
    – lhf
    Nov 3, 2015 at 10:43
  • $\begingroup$ @lhf: They are cognates. $\endgroup$
    – Lucian
    Nov 3, 2015 at 10:47

2 Answers 2

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It’s the scalar field of whatever vector space is under discussion.

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  • $\begingroup$ I saw that on Wikipedia, but that seems to correspond to the German "Skalarfeld", which in turn seems to differ from "Skalarraum", unless I misunderstood something. $\endgroup$ Nov 3, 2015 at 2:40
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    $\begingroup$ @Maasumi: You can’t expect necessarily to be able to translate by cognates. Skalarfeld is scalar field in the physical sense, e.g., the function that assigns to each point of some volume the temperature at that point. Field in the algebraic sense is Körper, and I’ve seen Skalarkörper and Grundkörper for the field of scalars of a vector space. I’ve seen Skalarraum only a few times, but in every case it’s referred to the field of scalars of some vector space – usually an infinite-dimensional space, though I don’t know whether that matters. $\endgroup$ Nov 3, 2015 at 2:45
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Perhaps "field of scalars", in the context of vector spaces.

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