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| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Matrix mortality problem | 1/1 | https://en.wikipedia.org/wiki/Matrix_mortality_problem | reference | science, encyclopedia | 2026-05-05T11:36:07.717257+00:00 | kb-cron |
In computer science, the matrix mortality problem (or mortal matrix problem) is a decision problem that asks, given a set of size m of n×n matrices with integer coefficients, whether the zero matrix can be expressed as a finite product of matrices from this set. The matrix mortality problem is known to be undecidable when n ≥ 3. In fact, it is already undecidable for sets of 6 matrices (or more) when n = 3, for 4 matrices when n = 5, for 3 matrices when n = 9, and for 2 matrices when n = 15. In the case n = 2, it is an open problem whether matrix mortality is decidable, but several special cases have been solved: the problem is decidable for sets of 2 matrices, and for sets of matrices which contain at most one invertible matrix.
== References ==
Bell, Paul; Potapov, Igor (2008-02-04). "On undecidability bounds for matrix decision problems". Theoretical Computer Science. Combinatorics, Automata and Number Theory. 391 (1): 3–13. doi:10.1016/j.tcs.2007.10.025. ISSN 0304-3975. Halava, Vesa (August 1997). Decidable and Undecidable Problems in Matrix Theory (Report). Turku Centre for Computer Science.>