Definition 13.1.14 (Norm in $\R^{n}$).label A norm in $\R^{n}$ is $\norm{\cd}{}:\R^{n}\to[0,\infty)$ such that
- (1)
$\norm{x}{}=0\iff x=0$
- (2)
$\norm{\lam x}{}=\abs{\lam}\norm{x}{}$ for all $\lam\in\R$
- (3)
$\norm{x+y}{}\leq\norm{x}{}+\norm{y}{}$
Definition 13.1.14 (Norm in $\R^{n}$).label A norm in $\R^{n}$ is $\norm{\cd}{}:\R^{n}\to[0,\infty)$ such that
$\norm{x}{}=0\iff x=0$
$\norm{\lam x}{}=\abs{\lam}\norm{x}{}$ for all $\lam\in\R$
$\norm{x+y}{}\leq\norm{x}{}+\norm{y}{}$
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