Linear factorization of \(\lambda\)-polynomial over quaternionic field (Q2732392)
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scientific article; zbMATH DE number 1623642
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Linear factorization of \(\lambda\)-polynomial over quaternionic field |
scientific article; zbMATH DE number 1623642 |
Statements
3 September 2001
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linear factorization
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quaternionic matrix
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main spectral sequence
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main spectrum
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lambda polynomial
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Jordan canonical form
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Linear factorization of \(\lambda\)-polynomial over quaternionic field (English)
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The problem of the linear factorization of any \(\lambda\)-polynomial \(\varphi(\lambda)\), where \(\varphi(\lambda) \in Q[\lambda]\) and \(Q[\lambda]\) being the ring of \(\lambda\)-polynomials over a quaternionic field \(Q\), is studied. Several theorems concerning the main spectral sequence and the main spectrum of \(\varphi(\lambda)\) including the factorization of \(\varphi(\lambda)\) into the products of linear factors are proved. Finally, it is postulated that any quaternionic matrix is similar to a complex Jordan canonical form and this can be derived by the linear factorization of the \(\lambda\)-polynomial.
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0.7586953639984131
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0.7451040744781494
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