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A.1.15 Orthogonal Transformation of Tensors
An orthogonal transformation transforms any vector into the vector , which we may denote as Recall that a tensor may be expressed in its spectral representation as per eq.(A.1.14-7). Each of its eigenvectors is transformed by into . Since eigenvalues of are invariant to orthogonal transformations, it follows that Thus, the transformation of the second-order tensor by is .