A Normal Form for Matrices Whose Elements are Holomorphic Functions |
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A₁ A₂ Ap+1 basis for 25.j canonical basis chains of length characteristic equation defined ELEMENTS ARE HOLOMORPHIC exists a matrix expressible in terms finite number finite set follows from Theorem FORM FOR MATRICES functions holomorphic greatest common divisor hence holomorphic functions identically zero index range integer j-th column Jordan form Jordan matrix Jordan normal form least common multiple limiting relation linear relation exists MATRICES OF HOLOMORPHIC MATRICES WHOSE ELEMENTS matrix S(z non-proportional throughout non-trivial solution number of terms order h partial basis principal ideal ring proper chains roots S₁ S₂ satisfies an equation satisfying the condition satisfying the equation satisfying the relations set of functions set of points set of vectors similarity transformation T₂ theory of matrices transformation T(z unimodular University of Wisconsin vector equation vector whose components W. G. LEAVITT W₁ Weyr characteristic Wrti Y₁ zero function zero of order