Zentralblatt MATH  REVIEW SUBMISSION FORM 
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Name:  
Miloslav Znojil  
Reviewer number:  
9689  
Email:  
znojil@ujf.cas.cz  
Item's zblNumber:  
DE015465442  
Author(s):  
Ipsen, Ilse C. F.:  
Shorttitle:  
Overview of relative sin theta theorems for invariant subspaces  
Source:  
J. Comput. Appl. Math. 123, No. 12, 131153 (2000).  
Classification:  
Primary Classification:  
 
Secondary Classification:  
 
Keywords:  
invariant subspace, rotation by perturbation, bounds on angle, dependence on eigenvalues, grading and scaling, reliable computation of eigenvectors  
Review:  
A complex square matrix is assumed to possess an invariant subspace, and a change of this subspace under a perturbation is measured by a certain ``pricipal" angle. For its sinus, a number of estimates is reviewed/listed for both the additive and multiplicative perturbations and different assumptions about the matrix. The review, a successor of similar surveys, offers another set of explanations why certain highaccuracy diagonalization methods are so reliable. It is well written and well understandable, with both the ideas and technicalities amply illustrated by the threedimensional or partitioned examples.  
Remarks to the editors:  