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We introduce Verblunsky-type coefficients of Toeplitz and Hankel matrices,which correspond to the discrete Dirac and canonical systems generated byToeplitz and Hankel matrices, respectively. We prove one to one correspondencesbetween positive-definite Toeplitz (Hankel) matrices and their Verblunsky-typecoefficients as analogs of the well-known Verblunsky's theorem. Severalinterconnections with the spectral theory are described as well.

Verblunsky-type coefficients for Dirac and canonical systems generated by Toeplitz and Hankel matrices, respectively