Sign up ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Is there a simple (possible inductive) proof for $|\mathbf{v}| \leq \sqrt{n}(|v_1|+|v_2|+ \cdots +|v_n|)$, $\mathbf{v} \in \mathbf{R}^n$? I've tried Cauchy-Schwarz, it doesn't seem to work.

share|cite|improve this question

1 Answer 1

up vote 14 down vote accepted

Since $|\mathbf{v}|^2=v_1^2+\ldots+v^2_n\leq (|v_1|+\ldots+|v_n|)(|v_1|+\ldots+|v_n|)$, it is enough to take the square root on both sides of the inequality. Remark: the prefactor $\sqrt{n}$ is superfluous.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.