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An orthogonal matrix is an invertible real matrix whose inverse is equal to its transpose.
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maximum of orthogonal vectors
$$v_1=(x_1,x_2,x_3\cdot\cdot\cdot,x_n)$$is such a vector. By changing its signs and positions of each component $x_i$, we can get different vectors. When n is odd, it's impossible for any of orthogona …