alusvälja

Alusväli is the Estonian term for base field in mathematics. It denotes the field of scalars over which a vector space, algebra or similar structure is defined. The base field determines how elements are scaled and how coordinates are expressed.

If V is a vector space over a base field F, then vectors are added and multiplied by scalars from F. A basis of V yields a representation of each vector as a linear combination of basis vectors with coefficients in F, and the dimension of V is the number of basis vectors. The choice of base field affects these properties; for example, a space can have different dimensions when viewed over different base fields (for instance the complex numbers viewed as a vector space over the real numbers has dimension 2).

Common base fields include the rational numbers Q, the real numbers R, the complex numbers C, and finite fields F_p. The base field also plays a central role in algebraic geometry and number theory, where objects like varieties or schemes are studied over a fixed base field, and the set of rational points depends on that field.

In mathematical literature in Estonian, alusväli is used to denote the base field. The term is part of the standard vocabulary of linear algebra, abstract algebra and algebraic geometry.