If A is $m \times n$ matrix such that $ m \geq n $ and B is a block matrix of form $ \begin{bmatrix}I & A \\ A^T & 0 \end{bmatrix} $, then what is the condition number of B in terms of singular values of A ?
Linear Algebra Question (SVD and Condition Number)
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linear-algebra
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0Let $A = U \Sigma V^T$ be an SVD of $A$. Then $B = \begin{bmatrix} U & \\ & V \end{bmatrix} \begin{bmatrix} I & \Sigma \\ \Sigma & 0 \end{bmatrix} \begin{bmatrix} U^T & \\ &V^T \end{bmatrix}$. We only need to find the condition number of matrix $\begin{bmatrix} I & \Sigma \\ \Sigma & 0 \end{bmatrix}$, which has diagonal blocks. Does anyone know an easy way to do this? – 2012-10-30