EDB — 11N

Exercises

1. [11N]If \(A∈ℂ^{m× n}\) we can define the induced norms

   \begin{equation} \| A\| _{p,q}{\stackrel{.}{=}}\max _{x∈ℂ^ n~ ,~ |x|_ p≤ 1} |Ax|_ q~ ~ .\label{eq:norme_ matrici_ C} \end{equation}

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   Show that \(\| A\| _{p,q} = \| \overline A\| _{p,q}\).