The paper defines a lexicographic total order on complex numbers and a Spectral and Nilpotent Ordering (SNO) for arbitrary matrices, claiming to extend majorization, Schur-Ostrowski, and operator convexity results to the complex domain.
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Matrix Ordering through Spectral and Nilpotent Structures in Totally Ordered Complex Number Fields
The paper defines a lexicographic total order on complex numbers and a Spectral and Nilpotent Ordering (SNO) for arbitrary matrices, claiming to extend majorization, Schur-Ostrowski, and operator convexity results to the complex domain.