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Linearly Dependent Sets of Algebraic Curvature Tensors with a Nondegenerate Inner Product

This paper examines the effects of linear dependence on a set of three algebraic curvature tensors constructed from symmetric bilinear forms with respect to a nondegenerate inner product, and proceeds to show the possibility for simultaneous orthogonal diagonalization of these forms. Additionally the capability for simultaneous diagonaliza-tion lends itself to some useful results regarding the eigenvalues of two of the forms.