Null has no effect.
Null is an adjective that refers to something lacking the force or value to have an effect. Null may be contrary to the law or lack the requirements related to the mode or substance.
For example: "The judge declared the measure announced by the governor null and void, considering that it violates the Constitution" , "The effort you make in training is null, and therefore you will not play the next game" , "The risks associated with this heater are null, since it works with infrared energy that does not pollute or consume oxygen" .
In everyday language, null – derived from the Latin nullus – is associated with nothing or none . If a person says that his knowledge of chemistry is null, he is referring to the fact that he has no ability whatsoever in this field. In a similar sense, someone who claims to have no interest in literature is a person who is not interested in anything related to books and letters.
Concept of nullity in law, politics and information technology
In law , nullity is a situation that invalidates a legal act. This means that, before being declared null, the act or rule was effective. A null marriage is one whose nullity is decreed due to the existence of an essential defect or vice in its celebration (if one of the parties has been forced to enter into it or if they conceal an illness from the other, for example).
In politics , a spoiled vote is a vote that has been cast incorrectly, either accidentally or intentionally. The inclusion of an unofficial ballot, more than one ballot, or foreign objects are grounds for invalidating a vote.
Computer programming uses the English version of the term null to indicate that a variable or object has not been defined or initialized. Depending on the language and the compiler or interpreter, it may be possible to avoid this case by means of automatic initialization, but this is not a recommended practice.
The null has no value.
The term in linear algebra
For linear algebra, which is the branch of mathematics that deals with systems of linear equations, matrices and vectors, as well as concepts such as linear transformations and vector spaces, a null vector is known as one whose modulus is zero (it is worth mentioning that it is also known as a zero vector ).
In Euclidean spaces (geometric spaces in which Euclid's Axioms can be satisfied), all the components of a null vector are precisely zero. In other words, if we take an n- dimensional Euclidean space, the vector will have all of its components (whose number will be equal to n ) with zero values and must be represented graphically as a point, since it will have no dimensions.
Null vectors have zero extension and, with respect to their direction, it is just as correct to say that they have none or that they have all of them simultaneously since null vectors are said to be orthogonal (sometimes understood as perpendicular ) to any other vector found in their space.
Properties of null vectors
Let's look at some of the properties of null vectors in linear algebra:
- Null vectors are the neutral elements of their vector space for internal addition operations, since adding them to any other vector in the same space always results in said vector.
- Null vectors result from the dot product (a binary operation involving two vectors in the same space that returns a number) by the number 0 and are a special case of a zero tensor.
- When performing a linear transformation f on a null vector, its preimage is known as the null space or kernel.
- If the only element of a vector subspace is a zero vector, it is called a zero space.