Further results on strongly core orthogonal matrix
Xiaoji Liu, Congcong Wang, Hongxing Wang
Abstract
Recently, Ferreyra and Malik (Core and strongly core orthogonal matrices. Linear Multilinear Algebra. 2021;1–16. doi:10.1080/03081087.2021.1902923) have proved that if A is strongly core orthogonal to B, then rk(A+B)=rk(A)+rk(B) and (A+B)◯#=A◯#+B◯#. But whether the reverse holds is an open question. In this paper, we solve the problem completely and get some new characterizations of strong core orthogonality.
Topics & Concepts
OrthogonalityCore (optical fiber)Multilinear mapMathematicsMultilinear algebraMatrix (chemical analysis)Algebra over a fieldOrthogonal matrixCombinatoricsPure mathematicsDiscrete mathematicsComputer scienceOrthogonal basisPhysicsChemistryJordan algebraGeometryAlgebra representationTelecommunicationsQuantum mechanicsChromatographyMatrix Theory and AlgorithmsAdvanced Mathematical Theories and ApplicationsMathematical Inequalities and Applications