Core and Core-EP Inverses of Tensors
For researchers in tensor algebra and matrix theory, this work extends core and core-EP inverses to tensors, but the contribution is incremental as it generalizes known matrix concepts.
The paper introduces definitions of core and core-EP inverses for complex tensors, investigates their characterizations and properties, and verifies results using a new algebraic approach that is also novel for matrices.
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.