adjugate
noun
ad·ju·gate ˈa-jə-gət 
plural adjugates
mathematics
: the mathematical transpose of a matrix in which each element is replaced by its cofactor
O. [T]aussky used an equivalent form of this fact to obtain a factorization of the adjugate of a matrix … and a result on commutativity … . Here we use it to prove the Cayley-Hamilton theorem and some new theorems.
William Watkins, American Mathematical Monthly, April 1975
compare adjoint sense 1 William Watkins, American Mathematical Monthly, April 1975
Word History
Etymology
derivative of adjugate, adjective, "related by a process of transposition," borrowed from Latin adjugāre "to join, attach," from ad- ad- + jugāre "to fasten, bind, marry," derivative of jugum "yoke"
First Known Use
1882, in the meaning defined above