vektorin

Vektorin is the genitive singular form of the Finnish noun vektori. It is used to express possession or association with a vector in Finnish sentences, for example “vektorin pituus” (the length of the vector) or “vektorin komponentit” (the vector’s components). The nominative form is vektori.

In mathematics and physics, a vector is an object that has both magnitude and direction and can be represented by coordinates in a space. A vector in R^n is typically written as v = (v1, v2, ..., vn). Operations include vector addition and scalar multiplication, which combine vectors linearly. The magnitude (length) of v is |v| = sqrt(v1^2 + ... + vn^2); a unit vector has length 1 and is obtained by dividing by its magnitude, v/|v| when |v| ≠ 0. Inner and outer products provide additional structure: the dot product gives a scalar, while the cross product (defined in three dimensions) yields a vector perpendicular to both operands. In linear algebra, vectors form a vector space and can be described relative to a basis by coordinates.

The genitive form “vektorin” thus serves a grammatical role in Finnish, while the underlying mathematical concept remains the same.