HNF

Hnf is an acronym that can refer to more than one topic in mathematics and biology. The most common meanings are Hermite normal form in mathematics and hepatocyte nuclear factor in biology.

Hermite normal form (HNF) is a canonical form for integer matrices under left multiplication by unimodular matrices. For an integer matrix A, there exists a unimodular matrix U such that UA is in Hermite normal form, which is a row-echelon–like, staircase arrangement with certain divisibility properties among the leading entries. There are variants of HNF depending on whether row operations or column operations are used. The form is unique for a given matrix and is widely used in computations involving integer linear algebra, such as solving systems of linear Diophantine equations, determining lattice bases, and testing equivalence of integer matrices.

Hepatocyte nuclear factor (HNF) refers to a family of transcription factors that regulate gene expression in liver and other tissues, notably the pancreas and kidney. Key members include HNF1, HNF3 (also known as FOXA1/FOXA2), HNF4, and HNF6 (ONECUT family). These factors play essential roles in organ development, differentiation, and metabolic regulation. Mutations or dysregulation of HNF genes, particularly HNF1A, HNF1B, and HNF4A, are associated with monogenic diabetes forms such as maturity-onset diabetes of the young (MODY) and can contribute to various metabolic or developmental disorders. The HNF family is studied for its contributions to tissue identity, gene regulatory networks, and disease mechanisms.