On idempotency and tripotency of linear combinations of two commuting tripotent matrices
Let \(T_{1}\) and \(T_{2}\) be two nonzero complex \({n}\times{n}\) matrices. Further let \(T_{1}\) and \(T_{2}\) be commuting tripotent, i.e. \(T_{1}T_{2}=T_{2}T_{1}\) and \(T_{i}^{3}=T_{i}\), \({i=1,2}\). Now for two complex numbers \(\lambda_{1}\) and \(\lambda_{2}\), put \({T}=\lambda_{1}T_{1}+\lambda_{2}T_{2}\). The authors present necessary and sufficient conditions for the tripotency and the idempotency of \(T\). They discuss the statistical importance of the results as well. They finish their paper by presenting some examples.
scientific article; zbMATH DE number 5522203