On the Remarkable Formula for Spectral Distance of Block Southeast Submatrix
عنوان مقاله: On the Remarkable Formula for Spectral Distance of Block Southeast Submatrix
شناسه ملی مقاله: JR_WALA-5-2_002
منتشر شده در در سال 1397
شناسه ملی مقاله: JR_WALA-5-2_002
منتشر شده در در سال 1397
مشخصات نویسندگان مقاله:
Alimohammad Nazari - Arak university of Iran
Atiyeh Nezami - Arak university of Iran
خلاصه مقاله:
Alimohammad Nazari - Arak university of Iran
Atiyeh Nezami - Arak university of Iran
This paper presents a remarkable formula for spectral distance of a given block normal matrix G_{D_۰} = \begin{pmatrix} A & B \\ C & D_۰ \end{pmatrix} to set of block normal matrix G_{D} (as same as G_{D_۰} except block D which is replaced by block D_۰), in which A \in \mathbb{C}^{n\times n} is invertible, B \in \mathbb{C}^{n\times m}, C \in \mathbb{C}^{m\times n} and D \in \mathbb{C}^{m\times m} with \rm {Rank\{G_D\}} < n+m-۱ and given eigenvalues of matrix \mathcal{M} = D - C A^{-۱} B as z_۱, z_۲, \cdots, z_{m} where |z_۱|\ge |z_۲|\ge \cdots \ge |z_{m-۱}|\ge |z_m|. Finally, an explicit formula is proven for spectral distance G_D and G_D_۰ which is expressed by the two last eigenvalues of \mathcal{M}.
کلمات کلیدی: Eigenvalues, Normal matrix, Distance norm
صفحه اختصاصی مقاله و دریافت فایل کامل: https://civilica.com/doc/1902998/