canonically conjugate variable
vartande-ye hanjârvârâné hamyuq
Fr.: variable canoniquement conjuguée
A generalized coordinate and its → conjugate momentum.
Canonically, adverb from → canonical; → conjugate; → variable.
hamyuq-e hamtâft (#)
A → complex number in which the → real part of the number remains the same, but i is replaced by -i. For example, the complex conjugate of x + iy is x - iy. Same as → conjugate complex number.
1) hamyuq (#); 2) hamyuqidan (#)
Fr.: 1) conjugué; 2) conjuguer
1) An element of a group related to a given element x by
y = z-1xz or zy = xz, where z is another element
of the group. Also known as → transform.
From L. conjugare "to join together," from → com- "together" + jugare "to join," from jugum "yoke," from PIE *yeug- "to join;" cf. Av. yaog- "to yoke, put to; to join, unite," Mid.Pers. jug, ayoxtan "to join, yoke," Mod.Pers. yuq "yoke," Skt. yugam "yoke," Hittite yugan "yoke;" Gk. zygon "yoke," zeugnyanai "to join, unite," O.C.S. igo, O.Welsh iou, Lith. jungas O.E. geoc.
Hamyuq, from ham- "together," → com- + yuq "yoke," from PIE *yeug- "to join," as above.
Fr.: angles conjugués
Two angles whose sum is 360° or 2π radians.
Fr.: axe conjugué
One of the two diameters of a conic, so related that a tangent at the end of one is parallel to the other.
conjugate complex number
adad-e hamtâft hamyuq (#)
Fr.: nombre complexe conjugé
The conjugate of a → complex number, expressed by ū = a - bi. The complex number and its conjugate have the same real part. Same as → complex conjugate.
Fr.: moment conjugué
If qj (j = 1, 2, ...) are generalized coordinates of a classical dynamical system, and L is its Lagrangian, the momentum conjugate to qj is pj = ∂L/∂q. Also known as canonical momentum.
Fr.: points conjugués
Two points positioned along the principal axis of a mirror or lens so that light coming from one focuses onto the other.
Fr.: rayon conjugué
Of an optical ray, the parallel ray that passes through the center of the → optical system.
Fr.: transpose conjugé
Of an m x n→ matrix A with → complex → elements, the n x m matrix A* obtained from A by taking the → transpose and then taking the → complex conjugate of each element. Same as → adjoint matrix or Hermitian transpose.
Fr.: conjugé hermitien
Math.: The Hermitian conjugate of an m by n matrix A is the n by m matrix A* obtained from A by taking the → transpose and then taking the complex conjugate of each entry. Also called adjoint matrix, conjugate transpose. → Hermitian operator.
Hermitian, named in honor of the Fr. mathematician Charles Hermite (1822-1901), who made important contributions to number theory, quadratic forms, invariant theory, orthogonal polynomials, elliptic functions, and algebra. One of his students was Henri Poincaré; → conjugate.