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A function \(\| \cdot \|\) is called a norm on \(\Cm\) if, for all vectors \(x\) and \(y\) in \(\Cm\)

1. \(\|x\| \geq 0\text{,}\) and \(\|x\|=0\) if and only if \(x=0\text{.}\)
2. \(\|\lambda x\| = |\lambda| \| x\|\) for any scalar \(\lambda \in \Cs\text{.}\)
3. \(\|x + y\| \leq \| x\| + \| y\|\) (triangle inequality).