Abstract
Let M be the backward identity matrix. A complex matrix G is perplectic if G is an isometry of the symmetric scalar product that is, for all column vectors x and y. The set of perplectic matrices P(n) forms a noncompact and nonconnected group. We show an Iwasawa-like decomposition for P(n), that is, we write every element G as a product KAN, where K is perplectic unitary, A is perplectic and diagonal having positive diagonal entries, and N is perplectic unipotent having a special block upper triangular structure.
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