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We examine the problem of equivalence of discrete time auto-regressive (AR) representations. Two AR representations are defined as fundamentally equivalent if their solution spaces or behaviors are isomorphic. Starting from the fact that the behavior of an AR representation, when considered over a finite time interval, depends on the algebraic structure of both the finite and the infinite elementary divisors of the underlying polynomial matrix we examine closely this structure and show that itdoi:10.1080/0020717031000123607 fatcat:v3a7hyr7efdfpn5pw7x43cqtxm