contragredience (kontragrediens)

[ two sets of variables be x, y, z, and §, η, ζ; and let the first set be transformed to X, Y, Z by the equations x = ax + by + cZ, y = dX + Y + Z, z = gX + hY + iz; then the contragredience of the two sets will consist in the second set ξ, η, 5 being subject to undergo a simultaneous transformation to E, H, Z, defined by the equations Ε = αξ + dy + gs, H = b + en + hs, Z = c + fn + is. A system of variables is said to be contragredient to another when it is subject to undergo simultaneously with the latter linear transformations of the contrary kind from it. That is to say, the matrix of transformation is turned over about its principal diagonal as an axis. J. J. Sylvester. contra harmonical (konträ-här-mon'i-kal), a. [ harmonical .] Opposed to or the op posite of harmonical. - Contra harmonical mean and proportion, the mean and proportion determined by the formula a: c = ( b - c ): ( a - b ).