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Let (K, M) be a linear matrix problem induced from a finite dimensional algebra Λ. Then an n×n matrix M in R(K, M) is indecomposable if and only if the number of links in the canonical form M(∞) of M is equal to M-dimn-1. On the other hand, the dimension of the endomorphism ring of M is equal to K-dimn-σ(M).