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What is the largest m such that there existv_{1}, ... ,v_{m}∈ ℝ^{n}such that for alliandj,if 1 ≤ i < j ≤ m, then ≤v_{i}⋅v_{j}= 0

I found a couple of solutions online.

http://mathoverflow.net/questions/31436/largest-number-of-vectors-with-pairwise-negative-dot-product

http://math.stanford.edu/~akshay/math113/hw7.pdf (problem 10. But it's basically the same solution as the one in the link above)

I kind of understand the contradiction but I don't get why there won't be a contradiction when you take m = n + 1. This is my first course in linear algebra, so far I've learnt about linear independence, subspaces, orthogonality but I'm notveryfamiliar with things like inner product spaces - only dot products. I need someone to explain this in simpler terms.

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# What is the largest number of mutually obtuse vectors in Rn?

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