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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6610 • Analysis of Numerical Methods I

Spring 2024 • Question 2

Question

Math 6610 • Analysis of Numerical Methods I Spring 2024 • Question 2

(Properties via SVD). Suppose \(A \in \mathbb {C}^{m \times m}\) has an SVD, \(A = U\Sigma V^*\). Find an eigenvalue decomposition of the \(2m \times 2m\) hermitian matrix (using information about SVD for \(A\)), \[ \begin {bmatrix} 0 & A^* \\ A & 0 \end {bmatrix}. \]

Raw LaTeX

(Properties via SVD).
Suppose \(A \in \mathbb{C}^{m \times m}\) has an SVD, \(A = U\Sigma V^*\). Find an eigenvalue decomposition of the
\(2m \times 2m\) hermitian matrix (using information about SVD for \(A\)),
\[
\begin{bmatrix}
0 & A^* \\
A & 0
\end{bmatrix}.
\]

Topic Tags

Eigenvalues, Spectral Radius, and Gershgorin Theorem Linear Programming and Optimization Singular Value Decomposition