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We analyze statistical properties of complex eigenvalues of random matrices$\hat{A}$ close to unitary. Such matrices appear naturally when consideringquantized chaotic maps within a general theory of open linear stationarysystems with discrete time. Deviation from unitarity are characterized by rank$M$ and eigenvalues $T_i, i=1,...,M$ of the matrix $\hat{T}=\hat{{\bf1}}-\hat{A}^{\dagger}\hat{A}$. For the case M=1 we solve the problem completelyby deriving the joint probability density of eigenvalues and calculating all$n-$ point correlation functions. For a general case we present the correlationfunction of secular determinants.Comment: 4 pages, latex, no figures, a few misprints are correcte

Spectra of random matrices close to unitary and scattering theory for discrete-time systems