Core and core-EP inverses of tensors

Specific definitions of the core and core-EP inverses of complex tensors are introduced. Some characterizations, representations and properties of the core and core-EP inverses are investigated. The results are verified using specific algebraic approach, based on proposed definitions and previously verified properties. The approach used here is new even in the matrix case. © 2019, SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional.