Please refer attachment for the problem. I need to prove that the given norm is COMPATIBLE. Please help me solve this.
Thank you!
Start in the following way: if $\displaystyle A=(a_{ij})\in\mathbb{K}^{n\times n}$ and $\displaystyle y=Ax$ with $\displaystyle x=(x_1,\ldots,x_n)^t$ and $\displaystyle y=(y_1,\ldots,y_n)^t$ then,
$\displaystyle \left\|{Ax}\right\|= \left\|{y}\right\|=\sum_{k=1}^nc_k{|y_k|}=\sum_{k= 1}^nc_k\left|{\sum_{j=1}^n}a_{kj}x_j\right|\leq \ldots$