About: Invariants of tensors

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In mathematics, in the fields of multilinear algebra and representation theory, the principal invariants of the second rank tensor are the coefficients of the characteristic polynomial , where is the identity operator and represent the polynomial's eigenvalues.

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rdfs:label	Invariants of tensors (en)
rdfs:comment	In mathematics, in the fields of multilinear algebra and representation theory, the principal invariants of the second rank tensor are the coefficients of the characteristic polynomial , where is the identity operator and represent the polynomial's eigenvalues. (en)
sameAs	Invariants of tensors Invariants of tensors
dbp:wikiPageUsesTemplate	dbt:Reflist
Subject	Tensors Invariant theory Linear algebra
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Invariants_of_tensors?oldid=1052390984&ns=0
Wikipage page ID	2147961 (xsd:integer)
page length (characters) of wiki page	9850 (xsd:nonNegativeInteger)
Wikipage revision ID	1052390984 (xsd:integer)
Link from a Wikipage to another Wikipage	Application of tensor theory in engineering Turbulence Tensors Cayley–Hamilton theorem George Batchelor Invariant theory Linear algebra Positive definiteness Characteristic polynomial Howard P. Robertson Tensor Eigenvalues and eigenvectors Newton's identities Walter Noll Elementary symmetric polynomial Finite strain theory Symmetric polynomial Faddeev–LeVerrier algorithm Helmholtz free energy David Hilbert Kármán–Howarth equation Strain energy density function Subrahmanyan Chandrasekhar Mathematics Multilinear algebra Representation theory
has abstract	In mathematics, in the fields of multilinear algebra and representation theory, the principal invariants of the second rank tensor are the coefficients of the characteristic polynomial , where is the identity operator and represent the polynomial's eigenvalues. More broadly, any scalar-valued function is an invariant of if and only if for all orthogonal . This means that a formula expressing an invariant in terms of components, , will give the same result for all Cartesian bases. For example, even though individual diagonal components of will change with a change in basis, the sum of diagonal components will not change. (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Invariants_of_tensors
is Wikipage redirect of	Second deviatoric invariant Tensor invariant Tensor invariants
is Link from a Wikipage to another Wikipage of	Lode coordinates BKL singularity Mooney–Rivlin solid Cauchy stress tensor Characteristic polynomial Howard P. Robertson Finite strain theory Invariant (mathematics) Invariant (physics) Neo-Hookean solid Herschel–Bulkley fluid
is foaf:primaryTopic of	http://en.wikipedia.org/wiki/Invariants_of_tensors

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