nonnullity

Nonnullity is a term encountered in mathematical literature as an informal way to describe a property of an object that is not identically zero. It is not a standard formal invariant across most disciplines, and its meaning can vary with context.

In functions and sequences, a function f: X -> Y is said to be nonnull if there exists x in X with f(x) ≠ 0. If Y is a vector space, this means f is not the zero function. A sequence (a_n) is nonnull if some term a_n ≠ 0.

In linear algebra, the term nullity is the dimension of the kernel; nonnullity is not a standard term, but when used informally some writers contrast a non-null map with a map possessing a nontrivial kernel. More precise language is preferred in formal contexts: a map is injective if its kernel is {0}, or it has trivial nullity.

In matrix terms, a matrix is nonnull if it contains at least one nonzero entry; equivalently, it is not the zero matrix. This usage tends to appear in informal writing or in specific applications and is not universal across texts.

In computer science, nonnull is widely used as an attribute to indicate that a reference or pointer will never be null; discussions of non-nullability appear in type systems and static analysis.

Etymology and note: The term derives from Latin nullus for “none” or “zero.” Because nonnullity is not a uniformly standardized concept, its meaning should be clarified within a given context.