Abstract
Symmetric factorizations of skew-symmetric real rational matrix functions are studied. In particular it is proved that generically a proper skew-symmetric real rational matrix mx m matrix function W(λ)=- W(λ) T with W(∞) invertible can be factorized minimally as W(λ)= L(λ) TDL (λ) for a real rational mx m matrix function L(λ). Applications are given concerning symmetric solutions of matrix quadratic equations.
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