# Relations Between the Field of Values of a Matrix and Those of its Schur Complements

### Ren-Cang Li

###
EECS Department

University of California, Berkeley

Technical Report No. UCB/CSD-94-849

December 1994

### http://www.eecs.berkeley.edu/Pubs/TechRpts/1994/CSD-94-849.pdf

Relations between the field of values of a matrix
*A* and those of its Schur complements are established. This work began with an attempt to get rid of pivoting from Gauss elimination under certain circumstances when the field of values
*F*(
*A*) does not contain the origin. The upper bound proved in this paper must be improved before it is of more practical use. However, the proof of the upper bound does provide an intuition of how a tight upper bound looks like.

BibTeX citation:

@techreport{Li:CSD-94-849, Author = {Li, Ren-Cang}, Title = {Relations Between the Field of Values of a Matrix and Those of its Schur Complements}, Institution = {EECS Department, University of California, Berkeley}, Year = {1994}, Month = {Dec}, URL = {http://www.eecs.berkeley.edu/Pubs/TechRpts/1994/5874.html}, Number = {UCB/CSD-94-849}, Abstract = {Relations between the field of values of a matrix <i>A</i> and those of its Schur complements are established. This work began with an attempt to get rid of pivoting from Gauss elimination under certain circumstances when the field of values <i>F</i>(<i>A</i>) does not contain the origin. The upper bound proved in this paper must be improved before it is of more practical use. However, the proof of the upper bound does provide an intuition of how a tight upper bound looks like.} }

EndNote citation:

%0 Report %A Li, Ren-Cang %T Relations Between the Field of Values of a Matrix and Those of its Schur Complements %I EECS Department, University of California, Berkeley %D 1994 %@ UCB/CSD-94-849 %U http://www.eecs.berkeley.edu/Pubs/TechRpts/1994/5874.html %F Li:CSD-94-849