Question 152
Let $\alpha$ be a real number. Suppose that there exists a $2024 \times 2024$ real matrix $(a_{ij})$ such that $\sum_{k=1}^{2024} a_{ik}^2 = 1$ for all $i$ and $\sum_{k=1}^{2024} a_{ik}a_{jk} = \alpha$ for all $i \neq j$.
Find the maximum possible value of $\alpha$.
(Nyamdavaa Amar)
Find the maximum possible value of $\alpha$.
(Nyamdavaa Amar)