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A relation R is antisymmetric if,

for all x and y, x R y and y R x => x == y.

I.e. no two different elements are mutually related.

Partial orders and total orders are antisymmetric. If R is also symmetric, i.e.

x R y => y R x


x R y => x == y

I.e. different elements are not related.
References in periodicals archive ?
As J is anti-symmetric and R is symmetric positive definite, substitute the controller of (8) into (9) yields
That means that when the unsymmetrical vibration mode shape of the object has been received as the result of the test, both symmetrical and anti-symmetric parts may be isolated on its basis.
LMS algorithm with LUT based multiplier optimization techniques Anti-symmetric Product Coding:
In my past works (with each of my theories being independent and self-contained; and I do not repeat myself ever), I have shown how all this can be accomplished: one is with the construction of an asymmetric metric tensor whose anti-symmetric part gives pure spin and electromagnetism, and whose differential structure gives an anholonomic, asymmetric connection uniquely dependent on x and dx (and hence x and the world-velocity u, giving a new kind of Finslerian space), which ultimately constructs matter (and motion) from pure kinemetric scratch.
nxn] denote the set of all n x m real matrices, the set of all n x n orthogonal matrices, the set of all n x n real symmetric matrices, the set of all n x n real anti-symmetric matrices, respectively; The symbols, [A.
can be replaced by symmetric (or anti-symmetric if sums of signal values will be replaced by differences) version (which requires m + 1 multiplications and M additions):
Using this transducer configuration, along with accurate synchronization of oscilloscope channels enables symmetric or anti-symmetric guided waves modes emphasis in recorded signals.
Another result is that the anti-symmetric state of the [[DELTA].
If we define a second-rank anti-symmetric tensor B by
As in [1], for reasons that will be clear later, we define the electromagnetic field tensor F via the torsion tensor of spacetime (the anti-symmetric part of the connection [GAMMA]) as follows:
In this framework, we produce the microspin tensor and the anti-symmetric part of the stress tensor as intrinsic geometric objects rather than alien additions to the framework of classical elasticity theory.

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