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  Volume 7, Issue 1, Article 17
On the Star Partial Ordering of Normal Matrices

    Authors: Jorma K. Merikoski, Xiaoji Liu,  
    Keywords: Star partial ordering, Normal matrices, Eigenvalues.  
    Date Received: 19/09/05  
    Date Accepted: 09/01/06  
    Subject Codes:

15A45, 15A18.

    Editors: Simo Puntanen,  

We order the space of complex $ ntimes n$ matrices by the star partial ordering $ starleq$. So $ mathbf{A}starleqmathbf{B}$ means that $ mathbf{A}^*mathbf{A}=mathbf{A}^*mathbf{B}$ and $ mathbf{A}mathbf{A}^*=mathbf{B}mathbf{A}^*$. We find several characterizations for $ mathbf{A}starleqmathbf{B}$ in the case of normal matrices. As an application, we study how $ mathbf{A}starleqmathbf{B}$ relates to $ mathbf{A}^2starleqmathbf{B}^2$. The results can be extended to study how $ mathbf{A}starleqmathbf{B}$ relates to $ mathbf{A}^kstarleqmathbf{B}^k$, where $ kgeq 2$ is an integer.

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