27th Conference of the International Linear Algebra Society (ILAS 2026)

Session

Symplectic Linear Algebra and Applications

MS 28

May 21, 2026, 2:00 PM

370. Structure-preserving Krylov Subspace Approximations for the Matrix Exponential of Hamiltonian Matrices

Heike Faßbender (TU Braunschweig, Institute for Numerical Analysis)

5/21/26, 2:00 PM

Symplectic Linear Algebra and Applications

Minisymposium Talk

It is well known that the matrix exponential $\exp(H)$ is symplectic whenever
$H \in \mathbb{R}^{2n \times 2n}$ is a Hamiltonian matrix. A matrix $H$ is called
Hamiltonian if it satisfies $HJ = (HJ)^{T},$
while a matrix $S$ is called symplectic (or $J$-orthogonal) if $S^{T} J S = J.$
Here, $J \in \mathbb{R}^{2n \times 2n}$ denotes $J =
\left [\begin{smallmatrix} 0 & I_n \ -I_n &...

163. On symplectic reduction of a matrix to upper $J$-Hessenberg form

Ahmed Salam (Université du Littoral-Côte d'Opale)

5/21/26, 2:25 PM

Symplectic Linear Algebra and Applications

Minisymposium Talk

In the context of computations of eignevalues and eignevectors, structure-preserving of a class of specific structured matrices, the reduction of a matrix to a $J$-Hessenberg condensed form is needed.\
Such reduction is based on symplectic similarity transformations.
It is a crucial step in the $SR$-algorithm (which is a $QR$-like algorithm), structure-preserving, for computing...

93. The $\phi-$Reversibility Problem for the Real Symplectic Group

Nicole Joy Datu (University of the Philippines Diliman)

5/21/26, 2:50 PM

Symplectic Linear Algebra and Applications

Minisymposium Talk

Let $G$ be a matrix group over a field $\mathbb{F}$ and $\phi: M_n(\mathbb{F}) \rightarrow M_n(\mathbb{F})$ be a map such that $\phi(A) \in G$ for all $A \in G.$
An element $A \in G$ is said to be $\phi-$reversible if there exists $P \in G$ such that $PAP^{-1}=\phi(A).$ If $P$ can be chosen to be an involution (i.e., $P^2=I),$ then $A$ is said to be strongly $\phi-$reversible. The...

84. On generalization of Williamson's theorem to real symmetric matrices

Hemant Mishra (Indian Institute of Technology (ISM) Dhanbad)

5/21/26, 3:15 PM

Symplectic Linear Algebra and Applications

Minisymposium Talk

Williamson's theorem states that if $A$ is a $2n \times 2n$ real symmetric positive definite matrix then there exists a $2n \times 2n$ real symplectic matrix $M$ such that $M^T A M=D \oplus D$, where $D$ is an $n \times n$ diagonal matrix with positive diagonal entries known as the symplectic eigenvalues of $A$. The theorem is known to be generalized to $2n \times 2n$ real symmetric positive...