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- W1508585242 abstract "We generalize the construction of canonical algebraic curvature tensors by self- adjoint 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 RA is 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." @default.
- W1508585242 created "2016-06-24" @default.
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- W1508585242 date "2010-01-01" @default.
- W1508585242 modified "2023-09-24" @default.
- W1508585242 title "The linear independence of sets of two and three canonical algebraic curvature tensors" @default.
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- W1508585242 doi "https://doi.org/10.13001/1081-3810.1386" @default.
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