Tripotency of a linear combination of two involutory matrices and a tripotent matrix that mutually commute
Copyright policy )Tripotency of a linear combination of two involutory matrices and a tripotent matrix that mutually commute
The authors study the tripotency of a linear combination of three matrices, which has a background in statistical theory. They demonstrate all the possible cases that lead to the tripotency of a linear combination of two involutory matrices and a tripotent matrix that mutually commute. By utilizing block technique and returning the partitioned matrices to their original forms, they derive the sufficient and necessary conditions such that a linear combination of three mutually commuting involutory matrices is tripotent. Editorial remark: For an addendum and corrigendum cf. also [\textit{E. Kişi}, ibid. 477, 211--212 (2015; Zbl 1332.15041)].
- University of Alberta Canada
- Harbin Engineering University China (People's Republic of)
- Harbin Institute of Technology China (People's Republic of)
Numerical Analysis, Algebra and Number Theory, Involutory matrix, commutativity, linear combination, Commutativity, Idempotent matrix, involutory matrix, Commutativity of matrices, Tripotent matrix, idempotent matrix, partitioned blocks, Discrete Mathematics and Combinatorics, Geometry and Topology, tripotent matrix, Partitioned blocks
Numerical Analysis, Algebra and Number Theory, Involutory matrix, commutativity, linear combination, Commutativity, Idempotent matrix, involutory matrix, Commutativity of matrices, Tripotent matrix, idempotent matrix, partitioned blocks, Discrete Mathematics and Combinatorics, Geometry and Topology, tripotent matrix, Partitioned blocks
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