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This problem is in Trefethen'book Numerical Linear Algebra

Suppose the $m\times n$ matrix $A$ has the form

$A=\begin{pmatrix}A_1\\A_2 \end{pmatrix}$

where $A_1$ is a nonsingular matrix of dimension $n\times n$ and $A_2$ is an arbitrary matrix of dimension $(m-n)\times n$. Prove $\|A^+\|_2\leq \|A_1^{-1}\|_2$. where $A^+=(A^*A)^{-1}A^*$

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@DavideGiraudo sorry – 89085731 Sep 20 '12 at 12:39
Is $\lVert \cdot\rVert$ the induced matrix norm by the euclian norm? – Davide Giraudo Sep 22 '12 at 20:49

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