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TanG
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Maximum number of vectors with bounds on inner products

Suppose there are 2n vectors $\{m_1,m_2,...,m_n\}$ and $\{\mu_1,\mu_2,...,\mu_n\}$. All vectors are in k-dimensional Euclid space $R^k$. The vectors satisfy: $$m_i \mu_j \leq 0, \quad \forall i<j $$ and $$ m_i \mu_i > 0, \quad \forall i.$$

What I want to prove: $n \leq 2k$.

Intuitively I think the bound $n \leq 2k$ is correct. It can be achieved by setting $m_i$ and $\mu_i$ to be the canonical base vectors and their negatives.

TanG
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