Structured strong linearizations from Fiedler pencils with repetition II

In this paper we give strong linearizations of a matrix polynomial P(λ)P(λ) preserving the skew-symmetry or T-alternating structure of P(λ)P(λ). The linearizations obtained are of the form SL(λ)SL(λ), where L(λ)L(λ) is a block-symmetric Fiedler pencil with repetition and S is a direct sum of blocks of the form I or −I, with I the identity matrix. This paper is a continuation of [2], where the corresponding problem for P(λ)P(λ) with a symmetric structure was studied and, as a consequence, the block-symmetric Fiedler pencils with repetition were characterized.