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- W4387151507 abstract "In this paper, we obtain tight lower bounds for the trace norm $Vert cdot Vert_1$ of some matrices with diagonal zero, in terms of the entry-wise $l_1$-norm (denoted by $Vert cdot Vert_{(1)}$). It is shown that on the space of nonzero real symmetric matrices $A$ of order $n$ with diagonal zero, the minimum value of the quantity $frac{Vert AVert_1}{Vert AVert_{(1)}}$ is equal to $frac{2}{n}$. The answer of the similar problem in the space of Hermitian matrices, is also obtained to be equal to $tan(frac{pi}{2n})$. The equivalent dual form of these results, give some upper bounds for the distance to the nearest diagonal matrix for a given symmetric or Hermitian matrix, when the distance is computed in the spectral norm." @default.
- W4387151507 created "2023-09-29" @default.
- W4387151507 creator A5091628990 @default.
- W4387151507 date "2023-09-26" @default.
- W4387151507 modified "2023-09-30" @default.
- W4387151507 title "Minimum trace norm of real symmetric and Hermitian matrices with zero diagonal" @default.
- W4387151507 doi "https://doi.org/10.48550/arxiv.2309.14958" @default.
- W4387151507 hasPublicationYear "2023" @default.
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