complex symmetric matrices 1real algebraic geometry 1semialgebraic dimension 1truncated toeplitz operators 1unitary equivalence 1
From the 1 of 2 linked papers with an AI index.
2 papers
math.FA2026
A Counterexample to the Gau--Wang--Wu Conjecture on Partial Isometries
Ryan O'Loughlin, Jani Virtanen
We disprove the conjecture of Gau, Wang and Wu that the numerical range of a finite-dimensional partial isometry, when circular, must be centred at the origin. More precisely, we p…
math.FA2026
Semialgebraic Dimension and Truncated Toeplitz Models for Complex Symmetric Matrices
Ryan O'Loughlin
The paper proves that for matrix sizes n ≥ 10, not every complex symmetric matrix can be expressed as a direct sum of truncated Toeplitz operators, using semialgebraic dimension te…