Bibliographic Details
| Title: |
Sums of skew-Hamiltonian or Hamiltonian dilatations. |
| Authors: |
de la Cruz, Ralph John L.1 (AUTHOR) rjdelacruz@math.upd.edu.ph, Salinasan, Jenny R.1 (AUTHOR) jsalinasan@math.upd.edu.ph, Tabigue, Mary Anne L.1,2 (AUTHOR) mltabigue@up.edu.ph |
| Source: |
Linear Algebra & its Applications. May2026, Vol. 737, p213-226. 14p. |
| Subjects: |
Complex matrices, Matrix decomposition, Linear algebra, Matrices (Mathematics), Symplectic geometry |
| Abstract: |
A 2 n × 2 n complex matrix A is Hamiltonian (respectively, skew-Hamiltonian) if J − 1 A T J = − A (respectively, J − 1 A T J = A) where J = [ 0 n I n − I n 0 n ]. We say that A is a Hamiltonian dilatation (respectively, skew-Hamiltonian dilatation) if A is Hamiltonian (respectively, skew-Hamiltonian) and is similar to [ a ] ⊕ [ − a ] ⊕ 0 2 n − 2 (respectively, [ a ] ⊕ [ a ] ⊕ 0 2 n − 2) for some 0 ≠ a ∈ C. We show that every 2 n × 2 n nonzero Hamiltonian not similar to J 2 (0) is a sum of n or fewer Hamiltonian dilatations and that for some Hamiltonian, n is sharp. We also show that every 2 n × 2 n nonzero skew-Hamiltonian is a sum of n or fewer skew-Hamiltonian dilatations, and for some skew-Hamiltonian, n is also sharp. Finally, we show that a Hamiltonian similar to J 2 (0) is a sum of two Hamiltonian dilatations and no fewer. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
