Nullvektori

Nullvektori, also known as the zero vector, is a fundamental concept in vector algebra and linear algebra. It is a vector that has a magnitude of zero and no specific direction. In mathematical notation, the nullvektor is often denoted by 0 or 0̅. The nullvektor is unique in that it is the only vector that, when added to any other vector, leaves that vector unchanged. This property is known as the additive identity.

In two-dimensional space, the nullvektor can be represented as (0, 0), and in three-dimensional space as (0, 0, 0). In general, the nullvektor in an n-dimensional space is represented as (0, 0, ..., 0), where there are n zeros.

The nullvektor is also the identity element for vector subtraction. Subtracting the nullvektor from any vector results in the original vector, while subtracting any vector from the nullvektor results in the negative of that vector.

In the context of linear transformations, the nullvektor is mapped to itself. This means that the nullvektor is always in the kernel (or null space) of any linear transformation.

The concept of the nullvektor is crucial in understanding vector spaces and linear transformations. It provides a reference point and simplifies many operations and proofs in linear algebra.