Skip to main content
Glite Dictionary
null space

null space

9.6
A set of vectors that a matrix sends to the zero vector
  • noun
  • /nʌl speɪs/
  • Specialized
translation icon : espacio nulo
  • In linear algebra, the null space of a matrix includes all its vectors that are mapped to the zero vector.

Examples

  • To understand the concept of a null space, one must first grasp how linear transformations function.

  • What's the dimension of the null space of a transpose?

  • It's it's it's null space is not just zero.

  • So a basis for the left null space of this matrix?

  • If A has a null space, then a transpose.

  • Finding the null space can help determine the solutions to a system of linear equations.

Synonyms

null set
vsnull space
  • Specialized
1 6.2

A set that has no members

is a subspace of vectors sent entirely to the zero vector by a linear map

Surface Forms

null space singular
null spaces plural

Morphology

null + space

The words 'null' (zero/no value) and 'space' (an area) would lead a learner to infer an 'empty' or 'zero' space, so the general idea is partially accessible from the parts. However, the precise mathematical meaning — a subspace of vectors mapped to the zero vector (which is a technical, non‑everyday notion and not simply 'empty') — is specialized and not fully predictable from B1 knowledge of the constituents.

Etymology

Null space comes from null meaning 'zero' and space meaning an area or set. Imagine a room where anything you put in becomes 'zero'; in math, the null space is the set of all vectors a matrix or function sends to the 'zero' vector, so they all end up as nothing.