Eigenvectors of a Rotation Matrix Export

@article{citeulike:6111981, abstract = {If a tensor is invariant under rotation about a fixed axis, the matrices representing the tensor and the rotation commute with each other. The two matrices have common eigenvectors, therefore a knowledge of eigenvectors of the rotation matrix provides us with some information about eigenvectors of the tensor. This result is applied to derive familiar representations of a transversely isotropic tensor of rank 2 and the elasticity tensor possessing tetragonal symmetry. Representation of the elasticity tensor belonging to a particular symmetry class can be achieved in an elegant manner. 10.1093/qjmam/hbp009}, author = {Ahmad, Faiz and Ahmad Khan, Riaz}, citeulike-article-id = {6111981}, citeulike-linkout-0 = {http://dx.doi.org/10.1093/qjmam/hbp009}, citeulike-linkout-1 = {http://qjmam.oxfordjournals.org/content/hbp009v1/.abstract}, citeulike-linkout-2 = {http://qjmam.oxfordjournals.org/content/hbp009v1/.full.pdf}, day = {12}, doi = {10.1093/qjmam/hbp009}, journal = {Q J Mechanics Appl Math}, keywords = {tensor}, month = {May}, pages = {hbp009+}, posted-at = {2009-11-14 17:47:20}, priority = {2}, title = {Eigenvectors of a Rotation Matrix}, url = {http://dx.doi.org/10.1093/qjmam/hbp009}, year = {2009} }

TY - JOUR ID - citeulike:6111981 L3 - citeulike-article-id:6111981 N2 - If a tensor is invariant under rotation about a fixed axis, the matrices representing the tensor and the rotation commute with each other. The two matrices have common eigenvectors, therefore a knowledge of eigenvectors of the rotation matrix provides us with some information about eigenvectors of the tensor. This result is applied to derive familiar representations of a transversely isotropic tensor of rank 2 and the elasticity tensor possessing tetragonal symmetry. Representation of the elasticity tensor belonging to a particular symmetry class can be achieved in an elegant manner. 10.1093/qjmam/hbp009 JF - Q J Mechanics Appl Math TI - Eigenvectors of a Rotation Matrix SP - hbp009 KW - tensor AU - Ahmad, Faiz AU - Ahmad Khan, Riaz PY - 2009/05/12/ UR - http://dx.doi.org/10.1093/qjmam/hbp009 ER -