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Application of the Dunford‐Taylor Integral to Isotropic Tensor Functions
Author(s) -
Itskov M.
Publication year - 2003
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200310381
Subject(s) - symmetric tensor , mathematics , tensor contraction , tensor (intrinsic definition) , cartesian tensor , tensor density , eigenvalues and eigenvectors , diagonal , tensor field , taylor series , mathematical analysis , tensor calculus , isotropy , pure mathematics , tensor product of hilbert spaces , space (punctuation) , algebra over a field , tensor product , exact solutions in general relativity , geometry , physics , linguistics , philosophy , quantum mechanics
In the present contribution closed‐form representations for isotropic tensor functions and their derivative are formulated using the Dunford‐Taylor integral. These representations are given in terms of eigenvalues of the tensor argument and are valid for all second‐order tensors defined as a linear mapping over the n‐dimensional real vector space. The solution obtained is especially useful for non‐symmetric tensor functions where representations based on the spectral decomposition in diagonal form cannot generally be applied.