image of the displacement vector at point s(x), mirror image of x, with respect to the horizontal plane. In algebraic terms, S is a matrix, of the same order as A. The main point is that S allows us to speak with mathematical precision of ‘symmetric' or ‘even' displacements (those such that v=Sv) and of ‘antisymmetric' or ‘odd' displacements (such that v = — Sv). More, any displacement v is the sum of its even and odd parts, for, if one introduces the matrices E and O by one has v=Ev+Ov for all v. Now we are ready to define symmetry, as a property of the structure. To say that if there is a node at x, there is a symmetrical one at s{x), is not enough. The trusses joining two pairs of symmetrical points also should be identical in their mechanical properties. All of this is said by the simply matrix relation i.e., in other words, the even and odd parts of u are given by solving two independent equations. To so trade off two problems for one would give no benefit if both problems (9)
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