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Since the introduction of majorization inby Hardy, Littlewood and Polya, several extensions of this concept have been studied in the literature. Recently, Kosuru and Saha [Cone type majorization and its strong linear preservers. Electron J Linear Algebra. 2020;36(36):511–518.] defined the concept of cone type majorization. In this paper, we focus on the study of the behavior of the linear preservers of majorization and cone type majorization under generalized inversion, namely, Drazin inversion and Moore-Penrose inversion. A characterization of these linear preservers, given by Ando [Majorization, doubly stochastic matrices and comparisons of eigenvalues. Linear Algebra Appl. 1989;118:163–248.] for majorization, and by Kosuru and Saha [Cone type majorization and its strong linear preservers. Electron J Linear Algebra. 2020;36(36):511–518.] for cone type majorization, prove to be crucial in our proofs.

Singular linear preservers of majorization and cone type majorization