In mathematics, the word null (from German: null[citation needed] meaning "zero", which is from Latin: nullus meaning "none") is often associated with the concept of zero, or with the concept of nothing.[1][2] It is used in varying contexts from "having zero members in a set" (e.g., null set)[3] to "having a value of zero" (e.g., null vector).[4]
In a vector space, the null vector is the neutral element of vector addition; depending on the context, a null vector may also be a vector mapped to some null by a function under consideration (such as a quadratic form coming with the vector space, see null vector, a linear mapping given as matrix product or dot product,[4] a seminorm in a Minkowski space, etc.). In set theory, the empty set, that is, the set with zero elements, denoted "{}" or "∅", may also be called null set.[3][5] In measure theory, a null set is a (possibly nonempty) set with zero measure.
A null space of a mapping is the part of the ___domain that is mapped into the null element of the image (the inverse image of the null element). For example, in linear algebra, the null space of a linear mapping, also known as kernel, is the set of vectors which map to the null vector under that mapping.
In statistics, a null hypothesis is a proposition that no effect or relationship exists between populations and phenomena. It is the hypothesis which is presumed true—unless statistical evidence indicates otherwise.[6]
See also
editReferences
edit- ^ ""null"". The Oxford English Dictionary, Draft Revision March 2004. 2004. Retrieved 2007-04-05.
- ^ "Definition of "null" adjective from the Oxford Advanced Learner's Dictionary". Oxford Advanced Learner's Dictionary 9th. 2016. Archived from the original on June 21, 2018. Retrieved 2018-06-21.
- ^ a b "What is null set? - Definition from WhatIs.com". WhatIs.com. Retrieved 2019-12-09.
- ^ a b Weisstein, Eric W. "Null Vector". mathworld.wolfram.com. Retrieved 2019-12-09.
- ^ "Math Symbols: Null Set". www.solving-math-problems.com. Archived from the original on July 31, 2009. Retrieved 2019-12-09.
- ^ Helmenstine, Anne Marie. "What Is the Null Hypothesis? Definition and Examples". ThoughtCo. Retrieved 2019-12-09.
 | This mathematics-related article is a stub. You can help Wikipedia by expanding it. |