Problem 1313 (difficulty: 5/10)

(a) Prove that all linear maps \(\displaystyle \R^p\to\R^q\) are Lipschitz.

(b) Prove that if \(\displaystyle A\in\mathrm{Hom}(\R^p,\R^p)\) is invertible, then \(\displaystyle \exists c>0 \, \forall x\in\R^p \, |A(x)| \ge c|x|\).

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