Nearest southeast submatrix that makes two prescribed‎ ‎eigenvalues

A. M. Nazari

Abstract


‎Given four complex matrices $A$‎, ‎$B$‎, ‎$C$ and $D$ where $A \in‎

‎\mathbb{C}^{n\times n}$ and $D \in \mathbb{C}^{m\times m} $ and‎

‎given two distinct arbitrary complex numbers $ \lambda_{1} $ and $‎

‎\lambda_{2} $‎, ‎so that they are not eigenvalues‎

‎of the matrix $A$‎,

‎we find a nearest matrix from the set of‎

‎matrices $ X \in \mathbb{C}^{m \times m } $ to matrix $D$ (with‎

‎respect to spectral norm) such that the matrix‎

‎$\begin{pmatrix}‎

‎A & B \\‎

‎C & X‎

‎\end{pmatrix} $‎

‎has two prescribed eigenvalues $ \lambda_{1} $ and $ \lambda_{2}$‎.


Refbacks

  • There are currently no refbacks.