A result about determinantal divisors |
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Authors: | Morris Newman |
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Institution: | Institute for algebra and combinatorics, and department of mathematics , University of california , Santa Barbara, CA, 93106 |
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Abstract: | Let Rbe a principal ideal ringRn the ring of n× nmatrices over R, and dk (A) the kth determinantal divisor of Afor 1 ? k? n, where Ais any element of Rn , It is shown that if A,BεRn , det(A) det(B:) ≠ 0, then dk (AB) ≡ 0 mod dk (A) dk (B). If in addition (det(A), det(B)) = 1, then it is also shown that dk (AB) = dk (A) dk (B). This provides a new proof of the multiplicativity of the Smith normal form for matrices with relatively prime determinants. |
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Keywords: | Numerical range tridiagonal envelope AMS Subject Classification:15A60 05C50 |
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