H. K. Mishra

Lidskii theorem for directional derivatives of symplectic eigenvalues

In this paper, we present a refinement of the symplectic Lidskii theorem for directional derivatives of symplectic eigenvalues, which is inspired by the work of Sendov [Electron. J. Linear Algebra 41(2025), 338-341]. We show that for a $2n \times 2n$ real positive definite matrix $A$ and symmetric matrices $H, K$ \begi...