Householder

A householder is a person who lives in a dwelling and has responsibility for its management. In everyday usage, the householder is the person in whose name the home is owned or rented, and often the primary respondent for household matters. The term is used without implying a particular gender or family role and can refer to the homeowner or the person who signs the lease or deed.

In demographic data collection, the householder is the reference person for the household. Census Bureau and many surveys designate the householder as the person who owns or rents the home, or, if several adults share, the one designated as the household head or primary respondent. The concept helps define household composition and relationships for data processing.

In mathematics, Householder transformation or Householder reflection is a linear transformation that reflects vectors across a plane or hyperplane. It is defined by H = I - 2 v v^T / (v^T v) for a nonzero vector v, and is used to introduce zeros below the diagonal in QR factorization, contributing to stable orthogonalization.

The term can also be a surname. The householder concept is historical and still used in various institutions to avoid the gendered term head of household.