An algorithm for simultaneous computation of the adjoint G(s) and determinant d(s) of the matrix polynomial s2J-sA 1-A 2 is presented, where J is a singular matrix. Both G(s) and d(s) are expressed relative to a basis...An algorithm for simultaneous computation of the adjoint G(s) and determinant d(s) of the matrix polynomial s2J-sA 1-A 2 is presented, where J is a singular matrix. Both G(s) and d(s) are expressed relative to a basis of Laguerre orthogonal polynomials. This algorithm is a new extension of Leverrier-Fadeev algorithm..展开更多
[目的]研究关于图的邻接特征多项式一些恒等式的证明.[方法]利用行列式的定义和基本性质.[结果]设G=(V,E,ω)是一个边赋权有向图,A(G)=(a ij)_(n×n)是其邻接矩阵.令Φ=(∅_(ij)(G,x))_(n×n)表示x I n-A(G)的伴随矩阵.本文给出...[目的]研究关于图的邻接特征多项式一些恒等式的证明.[方法]利用行列式的定义和基本性质.[结果]设G=(V,E,ω)是一个边赋权有向图,A(G)=(a ij)_(n×n)是其邻接矩阵.令Φ=(∅_(ij)(G,x))_(n×n)表示x I n-A(G)的伴随矩阵.本文给出了∅_(ij)(G,x)和G的一些子图的特征多项式之间等式的初等证明.[结论]本文给出的证明比已知的证明初等、简洁,并可以应用到其他类似的图多项式等式的证明.展开更多
The simultaneous diagonalization by congruence of pairs of Hermitian quaternion matrices is discussed. The problem is reduced to a parallel one on complex matrices by using the complex adjoint matrix related to each q...The simultaneous diagonalization by congruence of pairs of Hermitian quaternion matrices is discussed. The problem is reduced to a parallel one on complex matrices by using the complex adjoint matrix related to each quaternion matrix. It is proved that any two semi-positive definite Hermitian quaternion matrices can be simultaneously diagonalized by congruence.展开更多
文摘An algorithm for simultaneous computation of the adjoint G(s) and determinant d(s) of the matrix polynomial s2J-sA 1-A 2 is presented, where J is a singular matrix. Both G(s) and d(s) are expressed relative to a basis of Laguerre orthogonal polynomials. This algorithm is a new extension of Leverrier-Fadeev algorithm..
文摘[目的]研究关于图的邻接特征多项式一些恒等式的证明.[方法]利用行列式的定义和基本性质.[结果]设G=(V,E,ω)是一个边赋权有向图,A(G)=(a ij)_(n×n)是其邻接矩阵.令Φ=(∅_(ij)(G,x))_(n×n)表示x I n-A(G)的伴随矩阵.本文给出了∅_(ij)(G,x)和G的一些子图的特征多项式之间等式的初等证明.[结论]本文给出的证明比已知的证明初等、简洁,并可以应用到其他类似的图多项式等式的证明.
文摘The simultaneous diagonalization by congruence of pairs of Hermitian quaternion matrices is discussed. The problem is reduced to a parallel one on complex matrices by using the complex adjoint matrix related to each quaternion matrix. It is proved that any two semi-positive definite Hermitian quaternion matrices can be simultaneously diagonalized by congruence.
