= Equivariance of isotropic principal stresses
{title2=$\sigma_i(\lambda_{\pi(1)},\lambda_{\pi(2)},\lambda_{\pi(3)})=\sigma_{\pi(i)}(\lambda)$}
For an objective <material isotropy> law, permutation of the <principal stretches> permutes the labelled <principal stresses>. This follows by conjugating the <left stretch tensor> with signed permutation <rotation matrices>. Each principal stress is symmetric in the other two stretches, but need not be symmetric in all three. The law $\sigma=V^2$ provides the example $\sigma_i=\lambda_i^2$. In an invariant representation $\sigma=\beta_0I+\beta_1V+\beta_2V^2$, the scalar coefficients are symmetric functions of the unordered stretches.
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