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- W1488142898 abstract "We show that the weak and strong forms of the Generalized Spectral Conjecture (GSC) of Boyle and Handelman are equivalent. The GSC asserts that well understood necessary spectral conditions on a square matrix A over a subring S of the reals are sufficient for that matrix to be shift equivalent over S (in the weak form) or strong shift equivalent over S (in the strong form) to a primitive matrix over S. The foundation of this work is the recent result that the group NK_1(S) of algebraic K-theory exactly captures the refinement of shift equivalence over S by strong shift equivalence over S. The GSC remains open in general even in the case that S equals the real numbers." @default.
- W1488142898 created "2016-06-24" @default.
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- W1488142898 date "2016-06-01" @default.
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- W1488142898 title "Strong shift equivalence and the Generalized Spectral Conjecture for nonnegative matrices" @default.
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- W1488142898 doi "https://doi.org/10.1016/j.laa.2015.06.004" @default.
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