nullity

Nullity is a term used in several disciplines to indicate an absence or zero dimension of a specified object. In mathematics, especially linear algebra, nullity of a linear transformation or matrix is the dimension of its kernel—the set of all vectors that map to the zero vector. For a matrix A with n columns, the nullity is the dimension of the solution space to Ax = 0. The nullity is connected to the rank by the rank-nullity theorem: rank(A) + nullity(A) = n. This means nullity measures how many independent solutions exist to the homogeneous system Ax = 0. For example, a full-rank square matrix has nullity 0, while a matrix with more columns than its rank has positive nullity.

In law, nullity of marriage refers to a declaration that a marriage is invalid from the outset. It differs from divorce, which terminates a valid marriage. Jurisdictions specify grounds for nullity, which may include lack of consent, duress, fraud, previously existing marriages or incestuous relationships, or failure to meet legal formalities. The consequences often affect the legal status of the spouses, legitimacy of children, and allocation of property and parental rights, though rules vary by jurisdiction.

Other uses of the term are less common but may appear in philosophy or logic to denote a lack of meaningful content, or in computing contexts to describe a null result. The word derives from Latin nullus, meaning nothing. See also kernel, null space, rank-nullity theorem, annulment, and dissolution.