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- W1989749026 abstract "Let $$lambda ^{alpha _n } |lambda ^{alpha _{n - 1} } |...|lambda ^{alpha _2 } |lambda ^{alpha _1 } $$ , resp. $$lambda ^{beta _n } |lambda ^{beta _{n - 1} } |...|lambda ^{beta _2 } |lambda ^{beta _1 }$$ be the (given) invariant factors of the square matricesA, resp.B of ordern over the ring of germs of holomorphic functions in 0 such that detA(λ)B(λ)≠0, λ≠0. A description of all possible invariant factors $$lambda ^{gamma _n } |lambda ^{gamma _{n - 1} } |...|lambda ^{gamma _2 } |lambda ^{gamma _1 }$$ of the productC=AB is given in the following cases: (i)β 1 (or α1)≤2; (ii)β 3 = 0 (α3= 0); (iii) α1−α2, β1β m ≤1,α 2+1−β m+1−0. These results, which hold for arbitraryn, are complemented with a few results leading to the description of all possible exponents γ1,γ2,γ3,γ4 for arbitrary α1,α2,α3,α4 β1,β2,β3,β4 in the case where the ordern≤4." @default.
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- W1989749026 date "1993-06-01" @default.
- W1989749026 modified "2023-10-09" @default.
- W1989749026 title "The local invariant factors of a product of holomorphic matrix functions: The order 4 case" @default.
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- W1989749026 doi "https://doi.org/10.1007/bf01358957" @default.
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