# symmetric tensor

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## symmetric tensor

[sə¦me·trik ′ten·sər]
(mathematics)
A tensor that is left unchanged by the interchange of two contravariant (or covariant) indices.
References in periodicals archive ?
It is useful to embed these two degrees of freedom into a symmetric tensor field in order to build a local theory.
The 11 papers that emerged from the conference consider such topics as the exact limit of some cubic towers, optimal and maximal singular curves, on some bounds for symmetric tensor rank of multiplication in finite fields, a new proof of a Thomae-like formula for non-hyper-elliptic genus three curves, secret sharing schemes with strong multiplication and a large number of players from toric varieties, and field extensions and index calculations on algebraic curves.
Inspection shows that the matter-gravity tensor must be identified with the Rosenfeld-Belinfante symmetric tensor [3,4], thus complying with the intrinsic conservation property of the Einstein tensor as it should be.
It is easy to see that, for a = 0 (the ordinary Newtonian fluid), the force-stress tensor becomes a symmetric tensor and the couple-stress vector is zero.
The logarithm ln R is a skew symmetric tensor consisting of three independent elements of real numbers.
where K is a (0,2) covariant constant ([bar.[nabla]]K = 0) symmetric tensor field.
Under Voigt algebra, second-order symmetric tensors in 3 dimensions are represented as a 6-dimensional vectors and a fourth-order symmetric tensor is rewritten as a 6x6 matrix.
If T [member of] [S.sup.k] ([R.sup.n]), then the rank of a symmetric tensor [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is defined as
The number of independent components in a symmetric tensor can be obtained directly from Pascal's triangle.
Here [sigma] = [[sigma].sub.ij](x, y, z) is an inhomogeneous symmetric tensor of the head tissues conductivity.
Let [??] be a symmetric tensor of second order, with components [I.sub.ij] referred to a Cartesian reference frame {[[bar.i].sub.1], [[bar.i].sub.2], [[bar.i].sub.3]} and let [??] and [??] be any two directions.
In the second approach [19-21]--the one that we will employ in this paper--the TLS is characterized by a 3 x 3 symmetric tensor [T] and the coupling between [T] and [S] is made through a forth rank tensor of coupling constants denoted by [R].

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