nollavektoria

A nollavektoria, also known as a zero vector or null vector, is a mathematical object that exists in a vector space. It is unique within any given vector space and is characterized by having all of its components equal to zero. In Euclidean space, for example, the zero vector in two dimensions is (0,0), and in three dimensions it is (0,0,0).

The nollavektoria plays a crucial role in the structure of vector spaces. It serves as the additive identity, meaning that when it is added to any other vector in the space, the result is that other vector. This property is formally expressed as v + 0 = v, where v is any vector and 0 represents the nollavektoria.

Furthermore, any scalar multiple of the nollavektoria results in the nollavektoria itself. That is, for any scalar c, c * 0 = 0. This property is fundamental to understanding scalar multiplication within a vector space. The nollavektoria is distinct from a scalar zero, although they are often represented by the same symbol in certain contexts. The nollavektoria is a vector with magnitude zero and undefined direction, whereas a scalar zero is simply a numerical value. Its existence is a defining characteristic of any set that forms a vector space.