| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 4603972 | Linear Algebra and its Applications | 2006 | 8 Pages |
Abstract
Anexplicithomotopyisconstructedbetweentheidentitymatrixandanarbitraryrealmatrixwithpositivedeterminant.Theconstructionrequiresnoeigenvalueinformationandyieldsasmoothparameterizationforwhichthematrixdeterminantremainspositiveandvariesas a monotonic or unimodal function of the parameter. The key idea of the construction is that a simple formula smoothly transforms any product of two Householder reflections to the identity.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
