An upper bound for the determinant of a diagonally balanced symmetric matrix
arXiv:1212.1934h-index: 19
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This resolves a specific conjecture in matrix theory, providing a new inequality for a class of symmetric matrices.
The paper proves a conjectured determinantal inequality for diagonally balanced symmetric matrices, establishing an upper bound of 2(1-1/(n-1))^(n-1) for the ratio of the determinant to the product of diagonal entries.
We prove a conjectured determinantal inequality: \frac{\det J}{\prod_{i=1}^nJ_{ii}}\le 2(1-\frac{1}{n-1})^{n-1}, where $J$ is a real $n\times n$ ($n\ge 2$) diagonally balanced symmetric matrix.