Differentiability properties of rotationally invariant functions.

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F00%3A05010005" target="_blank" >RIV/67985840:_____/00:05010005 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Differentiability properties of rotationally invariant functions.
Original language description
Let f be a function on the set Lin of all tensors (=square matrices) on a vector space of arbitrary dimension. If f is rotationally invariant (with respect to the left and right multiplication by proper orthogonal tensors), it has a representation g through a symmetric even function of the signed singular values of the tensor argument A. It is shown that f is of class C^r, r=O,1,..., if and only if g of class C^r, and an inductive formula is given for the derivatives D^rf.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
<a href="/en/project/GA201%2F00%2F1516" target="_blank" >GA201/00/1516: Microstructure, relaxation, phase transitions, and hysteresis in shape memory alloys</a><br>
Continuities
Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year
2000
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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