The linear independence of sets of two and three canonical algebraic curvature tensors
ELA. The Electronic Journal of Linear Algebra, Tome 20 (2010), pp. 436-338.

Voir la notice de l'article dans Electronic Library of Mathematics

Summary: We generalize the construction of canonical algebraic curvature tensors by selfadjoint endomorphisms of a vector space to arbitrary endomorphisms. Provided certain basic rank requirements are met, we establish a converse of the classical fact that if A is symmetric, then R Ais an algebraic curvature tensor. This allows us to establish a simultaneous diagonalization result in the event that three algebraic curvature tensors are linearly dependent. We use these results to establish necessary and sufficient conditions that a set of two or three algebraic curvature tensors be linearly independent. We present the proofs of these results using elementary methods.
Classification : 15A21, 15A63
Mots-clés : algebraic curvature tensor, linear independence, simultaneous diagonalization 
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     title = {The linear independence of sets of two and three canonical algebraic curvature tensors},
     journal = {ELA. The Electronic Journal of Linear Algebra},
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     volume = {20},
     year = {2010},
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Diaz, Alexander; Dunn, Corey. The linear independence of sets of two and three canonical algebraic curvature tensors. ELA. The Electronic Journal of Linear Algebra, Tome 20 (2010), pp. 436-338. https://geodesic-test.mathdoc.fr/item/EEJLA_2010__20__a21/