论文标题
相对$ d $稳定矩阵的决定因素的一些范围
Some bounds for determinants of relatively $D$-stable matrices
论文作者
论文摘要
在本文中，我们研究了相对$ d $稳定的矩阵的类别，并提供了相对$ d $稳定性的条件。我们概括了著名的Hadamard不平等，以为相对$ d $稳定且相对添加$ d $稳定矩阵的决定因素提供上限。对于某些类别的$ D $稳定矩阵，我们估计矩阵光谱和虚轴之间的扇区差距。我们应用开发的技术来获得某些$ d $稳定矩阵的决定因素的上限，例如对角线稳定，对角占主导地位和矩阵，具有$ q^2 $尺寸。
In this paper, we study the class of relatively $D$-stable matrices and provide the conditions, sufficient for relative $D$-stability. We generalize the well-known Hadamard inequality, to provide upper bounds for the determinants of relatively $D$-stable and relatively additive $D$-stable matrices. For some classes of $D$-stable matrices, we estimate the sector gap between matrix spectra and the imaginary axis. We apply the developed technique to obtain upper bounds for determinants of some classes of $D$-stable matrices, e.g. diagonally stable, diagonally dominant and matrices with $Q^2$-scalings.
