For a class of pairs of entire matrix functions the null space of the natural analogue of the classical resultant matrix is described in terms of the common Jordan chains of the defining entire matrix functions. The main theorem is applied to two inverse problems. The first concerns convolution integral operators on a finite interval with matrix valued kernel functions and complements earlier results of [
]. The second is the inverse problem for matrix-valued continuous analogues of Szegő orthogonal polynomials.
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