Citation
Parker, Joseph A. Jr. (1976) The Matrix Equation F(A)X  XA = O. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/X6W2T505. https://resolver.caltech.edu/CaltechTHESIS:04072017144744158
Abstract
In this work, all matrices are assumed to have complex entries. The cases of F(A)  XA = O where F(A) is a polynomial over C in A and F(A) = (A^{*})^{1} are investigated. Canonical forms are derived for solutions X to these equations. Other results are given for matrices of the form A^{1}A^{*}.
Let a set solutions {X_{i}} be called a tower if X_{i+1} = F(X_{i}). It is shown that towers occur for all nonsingular solutions of (A^{*})^{1}X  XA = O if and only if A is normal. In contrast to this, there is no polynomial for which only normal matrices A imply the existence of towers for all solutions X of P(A)X  XA = O. On the other hand, conditions are given for polynomials P, dependent upon spectrum of A, for which only diagonalizable matrices A imply the existence of towers for all solutions X of P(A)X  XA = O.
Item Type:  Thesis (Dissertation (Ph.D.))  

Subject Keywords:  Mathematics  
Degree Grantor:  California Institute of Technology  
Division:  Physics, Mathematics and Astronomy  
Major Option:  Mathematics  
Thesis Availability:  Public (worldwide access)  
Research Advisor(s): 
 
Thesis Committee: 
 
Defense Date:  21 May 1976  
Funders: 
 
Record Number:  CaltechTHESIS:04072017144744158  
Persistent URL:  https://resolver.caltech.edu/CaltechTHESIS:04072017144744158  
DOI:  10.7907/X6W2T505  
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided.  
ID Code:  10133  
Collection:  CaltechTHESIS  
Deposited By:  Benjamin Perez  
Deposited On:  07 Apr 2017 22:41  
Last Modified:  05 Jan 2022 19:44 
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