---
title: "Matrix mortality problem"
chunk: 1/1
source: "https://en.wikipedia.org/wiki/Matrix_mortality_problem"
category: "reference"
tags: "science, encyclopedia"
date_saved: "2026-05-05T11:36:07.717257+00:00"
instance: "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.>