# Solution: 2013-04 Largest eigenvalue of a symmetric matrix

Let $$H$$ be an $$N \times N$$ real symmetric matrix. Suppose that $$|H_{kk}| < 1$$ for $$1 \leq k \leq N$$. Prove that, if $$|H_{ij}| > 4$$ for some $$i, j$$, then the largest eigenvalue of $$H$$ is larger than $$3$$.

The best solution was submitted by 김범수, 10학번. Congratulations!

Other solutions were submitted by 라준현(08학번, +3), 서기원(09학번, +3), 김호진(09학번, +3), 김범수(10학번, +3), 박훈민(13학번, +3), 노수현(13학번, +2). Thank you for your participation.

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