Nullvektorraum

The term "Nullvektorraum" refers to a vector space in linear algebra that contains only the zero vector. In mathematical notation, a vector space V over a field F is a null vector space if it satisfies the following conditions:

1. V is closed under vector addition: for any two vectors u and v in V, the sum u + v is also in V.

2. V is closed under scalar multiplication: for any vector u in V and any scalar c in F, the product cu is also in V.

3. The zero vector, denoted as 0, is in V.

4. For every vector u in V, there exists a vector -u in V such that u + (-u) = 0.

The primary characteristic of a null vector space is that it contains no other vectors besides the zero vector. This implies that the only linear combination of vectors in a null vector space is the zero vector itself. Null vector spaces are often used in theoretical contexts to illustrate the properties of vector spaces and linear maps.