Exercise10.4

Define the function \(\| \cdot \|_{A,1} : \Cm \to \R\) as \(\|x\|_{A,1} = \|Ax\|_1\) where \(\|\cdot \|_1\) is the usual 1-norm (a.k.a. “the taxicab norm”) on \(\Cm\text{,}\) and \(A \in \Cmm\) is non-singular. Is it true that \(\|Ax\|_1\) is a norm on \(\Cm\text{?}\)

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