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math.FA2025
Existence and Enumeration of Polynomially Transformed Matrices under Spectral and Nilpotent Constraints
Shih-Yu Chang
Matrix functions extend scalar function concepts to linear operators, offering a unified framework with broad applications in mathematics, science, and engineering. Classical defin…
math.FA2025
Matrix Ordering through Spectral and Nilpotent Structures in Totally Ordered Complex Number Fields
Shih-Yu Chang
Matrix inequalities play a pivotal role in mathematics, generalizing scalar inequalities and providing insights into linear operator structures. However, the widely used Löwner ord…
math.FA2024
Operator Characterization via Projectors and Nilpotents
Shih-Yu Chang
This paper explores operators with countable, continuous, and hybrid spectra, focusing on both finite dimensional and infinite dimensional cases, particularly in non-Hermitian syst…