Abstract
A set F = {A1,…, Am} of n×n matrices is said to be mortal if there exist integers k ≥ 1 and i 1, i 2,…, i k ∈ {1,…, m} such that A i 1A i 2 ••• A i k = 0. In that case F is also said to be k-length mortal.
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References
V. D. Blondel and J.N. Tsitsiklis, “When is a pair of matrices mortal?” Information and Processing Letters, 63, pp. 283–286 (1997).
V. D. Blondel and J.N. Tsitsiklis, “Complexity of stability and controllability of elementary hybrid systems,” Technical Report LIDS-P-2388, Laboratory for Information and Decision Systems, Massachusetts Institute of Technology, Cambridge, MA (1997). Also: Automatica, to appear.
O.Bournez and M. S. Branicky, “On the mortality problem for matrices of low dimensions”, Technical Report 98-01, VERIMAG, France (1998).
J. Cassaigne and J. Karhumaki, “Examples of undecidable problems for 2-generator matrix semi-groups,” Technical Report 57, Turku Center for Computer Science, University of Turku, Turku, Finland (1996).
M. Krom and M. Krom, “Recursive solvability of problems with matrices,” Zwitschr. f. math. Logik und Grundlagen d. Math, 35, pp. 437–442 (1989).
M. Krom and M. Krom, “More on mortality,” American Mathematical Monthly, 97, pp. 37–38 (1990).
M. S. Paterson, “Unsolvability in 3 × 3 matrices,” Studies in Applied Mathematics, XLIX, pp. 105–107 (1970).
P. Schultz “Mortality of 2 × 2 matrices,” American Mathematical Monthly, 84, pp. 463–464 (1977); correction, 85, p. 263, (1978).
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© 1999 Springer-Verlag London Limited
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Bournez, O., Branicky, M. (1999). On matrix mortality in low dimensions. In: Blondel, V., Sontag, E.D., Vidyasagar, M., Willems, J.C. (eds) Open Problems in Mathematical Systems and Control Theory. Communications and Control Engineering. Springer, London. https://doi.org/10.1007/978-1-4471-0807-8_14
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DOI: https://doi.org/10.1007/978-1-4471-0807-8_14
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