Abstract
The prime factorization problem of multivariate polynomial matrices was posed by Youla and Gnavi (IEEE Trans. Circuits and Sys., vol. 26, pp. 105-111) in 1979, and still remains open although there are some partial results covering certain special situations. In 1999, Z. Lin (J. Multidimensional Sys. and Sig. Proc., vol. 10, pp. 379-393) made a conjecture regarding prime factorizability of polynomial matrices in terms of their reduced minors. In 2001, Z. Lin and N.K. Bose (Linear Algebra and its Appl., vol. 338, pp. 125-138) studied several conjectures including earlier conjecture by Lin, and showed that they are indeed all equivalent. In this paper, we prove Lin's conjecture, and thereby prove the correctness of all the other conjectures posed by Lin and Bose.
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