Some New Developments of Matrix Inequalities(ⅰ)& Cauchy-Schwarz Type Inequalities and Schur Product Inequalities 矩阵不等式的一些新进展(Ⅰ)CauchySchwarz型不等式和Schur乘积不等式
The classical prediction of effective elastic properties for Cauchy mediums is recovered when the PST particle's diameter tends to infinity compared to the characteristic length of the micropolar matrix. 而当PST夹杂颗粒直径a与微极基体材料的特征长度lm相比很大时,微极理论对有效弹性模量预测的结果将趋近于采用传统Cauchy介质理论预测的结果。
Cauchy Matrix and Related Interpolation Problems Cauchy矩阵及其相关的插值问题
It is shows that if all subsystems are linear time-variant and the norm of subsystems 'Cauchy matrix satisfies reasonable conditions, the entire switched system is globally exponentially stable under arbitrary switching laws. 证明了如果所有的子系统是线性时变的,并且在系统的Cauchy矩阵的范数满足某种条件的情况下,整个切换系统在任意切换律下是全局指数稳定的。
In this paper, the Cauchy Principal Value integrals and the coefficients of free terms are computed directly, so the limitation of the number of nodes inside a sub-domain and the matrix inversion calculation in the rigid-body motion approach are avoided. 本文直接计算柯西主值积分和自由项系数,不但对于子域内包含的结点数目没有限制,而且避免了采用刚体位移法时的矩阵求逆运算。
In this paper, a fast algorithm for the Moore-Penrose inverse of an m × n Cauchy matrix with full column rank is given. 给出了求以秩为n的m×n阶Cauchy矩阵Moore-Penrose逆的快速算法,该算法的计算复杂度为O(mn)+O(n2)。
The left-inverse and the right-inverse of cauchy-type matrix Cauchy型矩阵的左逆及右逆
The inversion formula of a Cauchy matrix is proved in a different way from the adjoint matrix approach, which is by means of Complex Analysis and matrix equation theory. 用复分析和矩阵方程理论给出Cauchy矩阵求逆公式的一种新证明。
A formula of the left-inverse and right-inverse for an m × n Cauchy-type matrix is given if the solution of the linear system can be gotten. 通过方程组是否有解,给出了m×n阶Cauchy型矩阵左逆及右逆的一种求逆公式。
Through studying the encoding method of Cauchy RS code, it is found that Cauchy matrix plays an important role in encoding process. 通过分析柯西RS码的编码方式,柯西RS码在编码过程中柯西矩阵对编码效率有着极大的影响。