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arXiv · 1403.4535

Some new bounds for the Hadamard product and the Fan product of matrices

Qian-Ping Guo·Hou-Biao Li·Jin-Song Leng
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Abstract

If $A$ and $B$ are nonnegative matrices, a sharp upper bound on the spectral radius $ρ(A\circ B)$ for the Hadamard product of two nonnegative matrices is given, and the minimum eigenvalue $τ(A\star B)$ of the Fan product of two $M$-matrices $A$ and $B$ is discussed. In addition, we also give a sharp lower bound on $τ(A\circ B^{-1})$ for the Hadamard product of $A$ and $B^{-1}$. Several examples, illustrating that the given bound is stronger than the existing bounds, are also given.

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Qian-Ping Guo, Hou-Biao Li, Jin-Song Leng. 2014-03-18. Some new bounds for the Hadamard product and the Fan product of matrices. https://arxiv.org/abs/1403.4535

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