Suppose |A| = n. How many symmetric binary relations are there on A?

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orchestra answered 2 years ago

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Let A be an n × n real symmetric matrix with its row and column sums...

Let A be an n × n real symmetric matrix with its row and column sums both equal to 0. Let λ1, . . . , λn be the eigenvalues of A, with λn = 0, and with corresponding eigenvectors v1,...,vn (these exist because A is real symmetric). Note that vn = (1, . . . , 1). Let A[i] be the result of deleting the ith row and column. Prove that detA[i] = (λ1···λn-1)/n. Thus, the number of spanning...

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Suppose |A| = n. How many symmetric binary relations are there on A?

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