Tripotency of a linear combination of two involutory matrices and a tripotent matrix that mutually commute (Q448357)
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scientific article; zbMATH DE number 6078334
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Tripotency of a linear combination of two involutory matrices and a tripotent matrix that mutually commute |
scientific article; zbMATH DE number 6078334 |
Statements
Tripotency of a linear combination of two involutory matrices and a tripotent matrix that mutually commute (English)
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6 September 2012
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tripotent matrix
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involutory matrix
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idempotent matrix
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partitioned blocks
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commutativity
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linear combination
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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.NEWLINENEWLINEEditorial remark: For an addendum and corrigendum cf. also [\textit{E. Kişi}, ibid. 477, 211--212 (2015; Zbl 1332.15041)].
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