In symbolic computation, variables are stored as exact without numerical values to ensure precision throughout the calculations, which makes it an important area in computer algebra and scientific computing. A novel decomposition for third-order tensors within the t-product framework called tQDR decomposition is proposed to compute the outer inverse of symbolic tensors (tensors having polynomial entries and rational entries). In the process of introducing tQDR decomposition, a full rank factorization of tensors is also investigated. It is shown that many properties of full-rank decomposition of matrices (second-order tensors) do not hold in higher dimensions. Further, an algorithm inspired by the Leverrier-Faddeev algorithm is also introduced for efficiently computing the t-Moore–Penrose inverse of third-order symbolic tensors.
MSC Classification (2020): 15A09 , 15A69 , 68W30