Complex conference matrices and equi-isoclinic planes in Euclidean spaces

摘要

We demonstrate that if there exists a real symmetric conference matrix of order n , then there exists a complex symmetric conference matrix of order $$n-1$$ n - 1 . A v -set of equi-isoclinic planes in $$mathbb {R}^{n}$$ R n is a set of v planes spanning $$mathbb {R}^{n}$$ R n , each pair of which has the same non-zero angle $$rccos sqrt{lambda }$$ arccos λ . We prove that for any integer $$nge 5$$ n ≥ 5 for which there exists a complex symmetric conference matrix of order n , the maximum number of equi-isoclinic planes with angle arccos $$sqrt{rac{1}{n-1}}$$ 1 n - 1 in $$mathbb {R}^{n}$$ R n is equal to n .