@article{Ragosta_2020, title={Canonical Expressions of Algebraic Curvature Tensors}, volume={3}, url={https://journals.calstate.edu/pump/article/view/2253}, abstractNote={<p>Algebraic curvature tensors can be expressed in a variety of ways, and it is helpful to develop invariants that can distinguish between them. One potential invariant is the signature of <em>R</em>, which could be defined in a number of ways, similar to the signature of an inner product. This paper shows that any algebraic curvature tensor defined on a vector space<em> V</em> with dim(<em>V</em>) = <em>n</em> can be expressed using only canonical algebraic curvature tensors from forms with rank <em>k</em> or higher for any <em>k</em> in {2,...,<em>n</em>}, and that such an expression is not unique, eliminating some possibilities for what one might define the signature of <em>R</em> to be. We also provide bounds on the minimum number of algebraic curvature tensors of rank <em>k</em> needed to express any given <em>R</em>.</p>}, journal={The PUMP Journal of Undergraduate Research}, author={Ragosta, Kaitlin}, year={2020}, month={Feb.}, pages={52-61} }