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Math Help - How to prove that this Norm is COMPATIBLE?

  1. #1
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    How to prove that this Norm is COMPATIBLE?

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

    Thank you!
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    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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