A method of tensor.

diagonalise rank-two tensors or rank-four tensors in Voigt notation

Syntax

values, axes = T.eig()

Description

Eigenvalues are returned in ascending order. For rank two, the associated eigenvectors are antipodal vector3d axes in the tensor frame, arranged as rows after the tensor-array dimensions. For rank four the decomposition uses the 6-by-6 Voigt matrix and returns its numeric eigenvector matrix. Symmetric matrices use a real symmetric eigensolver.

Output

values eigenvalues, with the eigenvalue axis last
axes vector3d eigenvectors for rank two, numeric eigenvectors for rank four

See also

tensor.eigvals, Voigt, Kelvin

Signature

tensor.eig(self)

MATLAB’s tensor.eig

source

Citing this page. This page is part of the documentation of MTEX, a free and open source MATLAB toolbox for analyzing and modeling crystallographic textures. It was written by The MTEX Developers and is published at https://mtex-toolbox.github.io/tensor.eig_py.html. If you use MTEX, or reuse text or figures from this page, in your research, please cite

F. Bachmann, R. Hielscher, H. Schaeben: Texture Analysis with MTEX - Free and Open Source Software Toolbox, Solid State Phenomena 160 (2010), 63-68. 10.4028/www.scientific.net/SSP.160.63

BibTeX 
@article{bachmann2010mtex,
  author  = {F. Bachmann and R. Hielscher and H. Schaeben},
  title   = {Texture Analysis with MTEX - Free and Open Source Software Toolbox},
  journal = {Solid State Phenomena},
  volume  = {160},
  pages   = {63-68},
  year    = {2010},
  doi     = {10.4028/www.scientific.net/SSP.160.63},
  url     = {https://doi.org/10.4028/www.scientific.net/SSP.160.63}
}

Other papers describing specific MTEX methods are listed under Publications — please cite the one that best fits your application. The MTEX source code is licensed under the GNU General Public License v2.0; the text and figures of this documentation are licensed under CC BY 4.0, which permits reuse — including by automated systems — provided The MTEX Developers and this page are credited.