# Hamiltonian Matrix

In mathematics, a Hamiltonian matrix is a matrix that satisfies the condition that KA is Hermitian, where K is the skew-symmetric matrix

$K= \begin{bmatrix} 0 & I_n \\ -I_n & 0 \\ \end{bmatrix}$

and In is the n × n identity matrix. In other words, A is Hamiltonian if and only if

where * denotes the conjugate transpose. For real matrices, the above condition is fulfilled if KA is symmetric. In the vector space of all 2n × 2n matrices, Hamiltonian matrices form a subspace of dimension 2n2 + n.

Read more about Hamiltonian Matrix:  Properties, Hamiltonian Operators

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