Zero Vector
A Zero Vector is a vector composed of only zeroes.
- AKA: Null Vector.
- Context:
- It can be a member of a Zero Matrix.
- Example(s):
- [math]\displaystyle{ \vec(x) = (0, 0, 0) }[/math].
- …
- Counter-Example(s):
- a Unit Vector.
- a Non-Zero Vector.
- See: Vector Space, Euclidean Vector Space, Additive Identity.
References
2016
- (Wolfram MathWorld, 2016) ⇒ Weisstein, Eric W.,(1999-2016) "Null Vector." From MathWorld -- A Wolfram Web Resource. http://mathworld.wolfram.com/NullVector.html Retrieved 2016-6-18
- There are several meanings of “null vector” in mathematics. The most common usage is the n-dimensional null vector 0 is the n-dimensional vector of length 0 (i.e., the vector with n components, each of which is 0).
A second meaning of null vector when applied to a matrix A is a nonzero vector x with the property that Ax=0.
A third meaning of null vector when applied to a vector (which appears to be slightly nonstandard but is used for example in the Wolfram Language's FindIntegerNullVector function), is a nonzero vector a such that for a given vector x, the dot product satisfies a·x=0.
- There are several meanings of “null vector” in mathematics. The most common usage is the n-dimensional null vector 0 is the n-dimensional vector of length 0 (i.e., the vector with n components, each of which is 0).
2015
- (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/null_vector Retrieved:2015-2-7.
- In mathematics, a null vector is an element of a vector space that in some appropriate sense has zero magnitude.
In a vector space with a bilinear form, a vector that is self-orthogonal (i.e. on which the bilinear form is zero) is referred to as a null vector. In a seminormed vector space, it refers to a vector with zero seminorm. In contrast, the term zero vector refers to the unique additive identity of the vector space.
In contexts in which the only null vector is the zero vector (such as Euclidean vector space) or where there is no defined concept of magnitude, null vector may be used as a synonym for zero vector.
- In mathematics, a null vector is an element of a vector space that in some appropriate sense has zero magnitude.
2011
- http://en.wikipedia.org/wiki/Null_vector
- In linear algebra, the null vector or zero vector or empty vector is the vector (0, 0, …, 0) in Euclidean space, all of whose components are zero. It is usually written with an arrow head above or below it : [math]\displaystyle{ \vec{0} }[/math] or 0 or simply 0. A zero vector has arbitrary direction, but is orthogonal (ie perpendicular, normal) to all other vectors with the same number of components.
A different kind of vector, also called null vector or zero vector, arises in various generalizations of Euclidean space, as explained below.
Since the word null has a more general (and very different) meaning in computer programming, many programmers prefer the term zero vector to avoid confusion. For example, the statement if (MyVector == Null ) would intuitively be interpreted as if MyVector is a null pointer by many programmers, as opposed to if MyVector is a null/zero vector.
- In linear algebra, the null vector or zero vector or empty vector is the vector (0, 0, …, 0) in Euclidean space, all of whose components are zero. It is usually written with an arrow head above or below it : [math]\displaystyle{ \vec{0} }[/math] or 0 or simply 0. A zero vector has arbitrary direction, but is orthogonal (ie perpendicular, normal) to all other vectors with the same number of components.