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In [[computer science]], the '''matrix mortality problem''' (or '''mortal matrix problem''') is a [[decision problem]] that asks, given a finite set 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 problem|undecidable]] when ''n'' ≥ 3{{r|paterson}}. In fact, it is already undecidable for sets of 6
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