四元数体上矩阵弱直积与弱圈积的特征值和奇异值不等式

Inequalities of Eigenvalue and Singular Values for Weak Direct Products and Weak Circular Products of Mdtfices over the Real Quaternion Division Field

在实四元数体上研究矩阵弱直积与弱圈积的特征值与奇异值不等式，结合推广了的体上Ｃａｕｃｈｙ特征值交错定理，奇异值Ｔｈｏｍｐｓｏｎ交错定理，给出了体上弱直积的迹范数不等式，弱圈积的特征值与奇异值不等式，作为一个应用，给出了华罗庚矩阵的特征值估计，华氏定理进一步被证实。

This paper deals with the eigenvalue and singular inequalities of weak direct products andweak circular products over the real Quaterion Division field,joins the generalized cauchy's eigen-value interlacing theorem and Thom pson' s singular in terlacing theorem and gives out weak directproducts trace norm inequality and weak circular products singular inequality. For its application,theeigenvalues estamite of Hua Luogeng' s matrix is presented,thus,his theorem is proved by means of another method.