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Unsolvability in 3 × 3 Matrices
Author(s) -
Paterson Michael S.
Publication year - 1970
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm1970491105
Subject(s) - set (abstract data type) , zero (linguistics) , mathematics , matrix (chemical analysis) , finite set , product (mathematics) , algebra over a field , pure mathematics , combinatorics , discrete mathematics , computer science , mathematical analysis , geometry , chemistry , philosophy , linguistics , chromatography , programming language
A set of 3 × 3 matrices over the integers will be said to be mortal if the zero matrix can be expressed as a finite product of members of the set. It is shown in this paper that the problem of deciding whether a given finite set is mortal is recursively unsolvable.
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