Abstract
We establish an upper bound for the absolute value of the determinant of the Hadamard (elementwise) product of a unitary matrix and a general complex matrix. In the case that the general matrix is fixed and the unitary matrix is allowed to vary, this estimate is best possible. As a corollary, we obtain an upper bound for the absolute value of the determinant of the sum of two normal matrices with specified eigenvalues. This corollary supports the determinantal conjecture of Marcus and de Oliveira.
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