contragredient

Century Dictionary and Cyclopedia

1. In mathematics, said of a set of variables subject to undergo linear transformation simultaneously with another set (to which the first is said to be contragredient), the two transformations being inverse to one another Thus, let the two sets of variables be x, y, z, and ξ,η,ζ; and let the first set be transformed to X Y, Z by the equations
2. then the contragredience of the two sets will consist in the second set ξ,η,ζ being subject to undergo a simultaneous transformation to E, H, Z, defined by the equations

Wiktionary

1. adj. mathematics Generally, an object contragredient to another is the object inversed and transposed.
2. adj. mathematics A contragredient representation in linear algebra is the transpose of the former representation of an inverse object.
3. adj. mathematics A contragredient matrix is a transpose of an inverse matrix.