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Underlying field of a vector space

Ciro Santilli (@cirosantilli, 37) Mathematics Area of mathematics Algebra Linear algebra Vector space
Updated 2025-07-16  0 By others on same topic  0 Discussions Create my own version
Every vector space is defined over a field.
E.g. in R3, the underlying field is R, the real numbers. And in C2 the underlying field is C, the complex numbers.
Any field can be used, including finite field. But the underlying thing has to be a field, because the definitions of a vector need all field properties to hold to make sense.
Elements of the underlying field of a vector space are known as scalar.

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