4 papers
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…
Spectral and Nilpotent Matrix Orderings: Comparison and Applications in Dynamic Systems
Shih-Yu Chang
In our earlier work, we proposed the \emph{Spectral and Nilpotent Ordering} (SNO) as a new framework that extends matrix comparison beyond the Hermitian setting by incorporating bo…
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 or…
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…