NULL SPACE Meaning and
Definition
-
The term "null space" refers to a fundamental concept in linear algebra that describes the set of all vectors that are mapped to zero when a linear transformation is applied. In other words, it is the collection of vectors that are annihilated or "nullified" by the given linear transformation.
Mathematically, if we have a linear transformation T: V → W, where V and W are vector spaces, then the null space of T, denoted as null(T), is the set of all vectors v in V such that T(v) = 0. In simpler terms, it represents the pre-image of the zero vector under the given linear transformation.
The null space is an important concept in linear algebra as it helps understand the behavior and properties of linear transformations. It plays a significant role in determining the solutions to systems of linear equations, as the solutions can be found by finding vectors that belong to the null space of the associated matrix of coefficients.
Additionally, the null space provides insights into the dimension and rank of a linear transformation. The dimension of the null space is related to the nullity of T, which is the number of vectors in the null space. The dimension of the null space, along with the dimension of the image space, adds up to the dimension of the domain vector space. Moreover, the null space can be utilized in finding a basis for the kernel, which is a subspace formed by all linear combinations of vectors in the null space.
In conclusion, the null space is the set of vectors that yield zero when a linear transformation is applied and encompasses various crucial aspects in linear algebra.
Common Misspellings for NULL SPACE
- bull space
- mull space
- jull space
- hull space
- nyll space
- nhll space
- njll space
- nill space
- n8ll space
- n7ll space
- nukl space
- nupl space
- nuol space
- nulk space
- nulp space
- nulo space
- null apace
- null zpace
- null xpace
- nullspace
Etymology of NULL SPACE
The term "null space" originated from mathematics and specifically linear algebra.
Etymologically, "null" derives from the Latin word "nullus", meaning "none" or "zero". In linear algebra, the null space refers to the set of all vectors that, when multiplied by a given matrix, produce a zero vector. Therefore, the concept of the null space emerged from the idea of a space consisting of vectors resulting in zero or having no effect when operated upon by the matrix.
Infographic
Add the infographic to your website:
