How to prove that this Norm is COMPATIBLE?

**mathews** · May 20th 2011, 05:58 AM

Please refer attachment for the problem. I need to prove that the given norm is COMPATIBLE. Please help me solve this.

Thank you!

**FernandoRevilla** · May 20th 2011, 07:10 AM

Start in the following way: if $A=(a_{ij})\in\mathbb{K}^{n\times n}$ and $y=Ax$ with $x=(x_1,\ldots,x_n)^t$ and $y=(y_1,\ldots,y_n)^t$ then,
$\left\|{Ax}\right\|= \left\|{y}\right\|=\sum_{k=1}^nc_k{|y_k|}=\sum_{k= 1}^nc_k\left|{\sum_{j=1}^n}a_{kj}x_j\right|\leq \ldots$

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