nollskalaren

Nollskalaren is a term found in Swedish-language mathematical texts that refers to the zero scalar—the scalar value zero used in scalar multiplication and related operations. Etymologically, it combines noll (zero) with skalaren (the scalar).

In linear algebra, scalar multiplication combines a scalar with a vector to produce a new vector. The zero scalar has a defining role: applying it to any vector v yields the zero vector, written as 0·v = 0. This makes the zero scalar the absorbing element for scalar multiplication in the usual sense. It also allows a concise description of the zero map: when a linear operator is defined by f(v) = αv, setting α = 0 yields the zero operator f(v) = 0 for all v.

Beyond basic vector spaces, the concept is used to illustrate scaling and normalization processes, and it appears in discussions of linear transformations, eigenvalues, and function definitions such as f(x) = αx, where choosing α = 0 produces the trivial (zero) function.

Notes on usage and scope: nollskalaren is not a separate mathematical object, but a label for the zero scalar within Swedish pedagogy and literature. As in other languages, the term emphasizes the special role of zero in scaling and linear structure. In multilingual contexts, the same idea is typically expressed simply as “the zero scalar.”

See also: scalar, scalar multiplication, zero vector, linear transformation, zero function.