# Binet-Cauchy or Cauchy-Binet?

The Cauchy-Binet formula in linear algebra gives the determinant of a square matrix $AB$ for rectangular matrices $A,B$ of appropriate shape in terms of the determinants of the submatrices of $A,B$. (See the linked Wikipedia page for the specifics.) In the special case of $A$ with two columns, this reduces to a summation identity which Wikipedia in turn refers to as the Binet-Cauchy identity.

Why Cauchy-Binet for the determinant formula and Binet-Cauchy for the special case?

• Who knows the mind of Wikipedia? :) Shafarevich-Remizov (p.69) refer to the identity as still Cauchy-Binet, and Dym (p.103), Lancaster (p.39), etc., refer to the formula as Binet-Cauchy, which is in line with the alphabetical convention in mathematics but is not always followed. – Conifold Mar 7 '17 at 21:24
• One would expect to alphabetize the names only if it comes from a joint paper by the two authors Binet and Cauchy. For principles/theorems with two mathematicians contributing separately, more common would be chronological order: Cauchy-Buniakovsky-Schwarz inequality; Heine-Borel theorem, etc. – Gerald Edgar Mar 8 '17 at 1:01