ABSTRACT

The numerical radius of a matrix is a scalar quantity that has many applications in the study of matrix analysis. Due to the difficulty in computing the numerical radius, inequalities bounding it have received a considerable attention in the literature. In this article, we present many new inequalities for the numerical radius of accretive matrices. The importance of this study is the presence of a new approach that treats a specific class of matrices, namely the accretive ones. While some of these inequalities can be considered as refinements of other existing ones, others present new insight to some known results for positive matrices.

中文翻译：

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增生矩阵的数值半径

抽象的

矩阵的数值半径是一个标量，在矩阵分析的研究中有许多应用。由于难以计算数值半径，限制它的不等式在文献中受到相当大的关注。在本文中，我们提出了增生矩阵数值半径的许多新不等式。这项研究的重要性在于存在一种新方法，该方法可以处理特定类别的矩阵，即增生矩阵。这些不等式中的一些不等式可以看作是对其他现有不等式的改进，而其他不等式则为正矩阵的一些已知结果提供了新的见解。