A commutativity relation for submatrices of the inverse of a Sylvester matrix

Luo Y.; Schwerdtfeger U.; Hill R.

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A commutativity relation for submatrices of the inverse of a Sylvester matrix

机译：Sylvester矩阵逆的子矩阵的可交换性关系

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摘要

We take the inverse of a Sylvester matrix of two coprime polynomials of degree m and study the family of m×m submatrices formed from consecutive columns of the bottom m rows. We prove that these matrices commute and in the course of the proof we find a similar relation for Bezoutian matrices related to the polynomials.

机译：我们采用度数为m的两个互质多项式的Sylvester矩阵的逆，并研究由底部m行的连续列形成的m×m子矩阵族。我们证明这些矩阵是通勤的，并且在证明过程中我们发现与多项式有关的Bezoutian矩阵具有相似的关系。

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《Linear Algebra and its Applications》 |2012年第10期|共13页
作者
Luo Y.; Schwerdtfeger U.; Hill R.;
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正文语种 eng
中图分类线性代数;
关键词
Bezoutian; Sylvester matrix; Toeplitz matrix;

机译：Bezoutian;Sylvester矩阵;Toeplitz矩阵;

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专利

1. A commutativity relation for submatrices of the inverse of a Sylvester matrix [J] . Luo Y., Schwerdtfeger U., Hill R. Linear Algebra and its Applications . 2012,第10期

机译：Sylvester矩阵逆的子矩阵的可交换性关系
2. On the fixed-point type Sylvester matrix equations over complete commutative dioids [J] . Hashemi Benham, Mirzaei Khalilabadi Mahtab, Tavakolipour Hanieh The Electronic Journal of Linear Algebra . 2015,第1期

机译：关于完全可交换双曲面的不动点型Sylvester矩阵方程
3. Rank and inertia of submatrices of the Moore-Penrose inverse of a Hermitian matrix [J] . Tian Yongge The Electronic Journal of Linear Algebra . 2010,第1期

机译：Hermitian矩阵的Moore-Penrose逆子矩阵的秩和惯性
4. Commutative properties of invertible multipliers in relation to representation of their inverses [C] . Diana T. Stoeva, Peter Balazs International Conference on Sampling Theory and Applications . 2017

机译：与其反转表示中可逆乘法器的换向性质
5. MATRIX COMMUTATIVITY AND MATRIX COMMUTATORS. [D] . MARYAK, JOHN LOUIS. 1972

机译：矩阵可交换性和矩阵交换器。
6. Multiple Testing of Submatrices of a Precision Matrix with Applications to Identification of Between Pathway Interactions [O] . Yin Xia, Tianxi Cai, T. Tony Cai -1

机译：精确矩阵的子矩阵的多重测试及其在通路相互作用之间的识别中的应用
7. A commutativity relation for submatrices of the inverse of a Sylvester matrix [O] . Luo Yousong, Schwerdtfeger Uwe, Hill Robin 2012

机译：Sylvester矩阵逆的子矩阵的可交换性关系

A commutativity relation for submatrices of the inverse of a Sylvester matrix

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