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

Famous quotes containing the word matrix:

    “As all historians know, the past is a great darkness, and filled with echoes. Voices may reach us from it; but what they say to us is imbued with the obscurity of the matrix out of which they come; and try as we may, we cannot always decipher them precisely in the clearer light of our day.”
    —Margaret Atwood (b. 1939)