Hamiltonian matrix

In mathematics, a Hamiltonian matrix is a $2 n$ -by- $2 n$ matrix $A$ such that $JA$ is symmetric, where $J$ is the skew-symmetric matrix

J={\begin{bmatrix}0_{n}&I_{n}\\-I_{n}&0_{n}\\\end{bmatrix}}

and $I n$ is the $n$ -by- $n$ identity matrix. In other words, $A$ is Hamiltonian if and only if $(JA) T = JA$ where $() T$ denotes the transpose.^[1]

^ Ikramov, Khakim D. (2001), "Hamiltonian square roots of skew-Hamiltonian matrices revisited", Linear Algebra and its Applications, 325: 101–107, doi:10.1016/S0024-3795(00)00304-9.

[ikramov-1] Ikramov, Khakim D. (2001), "Hamiltonian square roots of skew-Hamiltonian matrices revisited", Linear Algebra and its Applications, 325: 101–107, doi:10.1016/S0024-3795(00)00304-9.

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