Coxeter transform and strictly regular matrices (Q881020)
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scientific article; zbMATH DE number 5155470
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Coxeter transform and strictly regular matrices |
scientific article; zbMATH DE number 5155470 |
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Coxeter transform and strictly regular matrices (English)
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21 May 2007
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The Coxeter transform of an \(n\)-by-\(n\) matrix \(A\) is a product of \(n\) matrices \(R_1\cdots R_n\), where \(R_i=R_i(A):=I-AE_{ii}\). The article characterizes which invertible \(n\)--by--\(n\) matrices can be written as a Coxeter transform of some \(A\), and when can a (possibly noninvertible) matrix be written uniquely in this way. The answer is obtained in terms of nonvanishing of all principal minors.
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reflection, pseudoreflection
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principal minor
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strictly regular matrix
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almost strictly regular matrix
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0.7170301079750061
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0.7012214660644531
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0.6935211420059204
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