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On Rank Subtractivity Between Normal Matrices  
 
  Authors: Jorma K. Merikoski, Xiaoji Liu,  
  Keywords: Rank subtractivity, Minus partial ordering, Star partial ordering, Sharp partial ordering, Normal matrices, EP matrices.  
  Date Received: 13/07/2007  
  Date Accepted: 05/02/2008  
  Subject Codes:

15A45, 15A18.

  
  Editors: Fuzhen Zhang,  
 
  Abstract:

The rank subtractivity partial ordering is defined on $ mathbb{C}^{ntimes n}$ ($ ngeq 2$) by $ mathbf{A}leq^-mathbf{B} Leftrightarrow {mathrm{rank}}(mathbf{B}-mathbf{A}) = {mathrm{rank}}mathbf{B}-{mathrm{rank}}mathbf{A}$, and the star partial ordering by $ mathbf{A}le^*mathbf{B}Leftrightarrow mathbf{A}^*mathbf{A} = mathbf{A}^*mathbf{B} mathrel{land}mathbf{A}mathbf{A}^* = mathbf{B}mathbf{A}^*$. If $ mathbf{A}$ and $ mathbf{B}$ are normal, we characterize $ mathbf{A}leq^-mathbf{B}$. We also show that then $ mathbf{A}leq^-mathbf{B}mathrel{land}mathbf{AB}= mathbf{BA} Leftrightar... ...arrow mathbf{A} leq^-mathbf{B} mathrel{land}mathbf{A}^2leq^-mathbf{B}^2$. Finally, we remark that some of our results follow from well-known results on EP matrices. ;


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