Triangularizing matrix polynomials
Triangularizing matrix polynomials
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DOI：
10.1016/j.laa.2013.05.006
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发表时间：
2013-10
影响因子：
1.1
通讯作者：
Leo Taslaman;F. Tisseur;I. Zaballa
中科院分区：
文献类型：
--
作者：
Leo Taslaman;F. Tisseur;I. Zaballa
对于代数闭域 F，我们证明任何矩阵多项式 P (λ)∈ F [λ] n× m, n⩽ m 都可以简化为三角形形式，同时保留次数以及有限和无限初等除数。我们还描述了在实数上可三角化的实矩阵多项式，并表明那些不可三角化的多项式是具有大小为 1× 1 和 2× 2 的对角块的拟三角化的。我们提出的证明解决了从初等除数列表开始构建三角矩阵多项式的结构化逆问题。
For an algebraically closed field F, we show that any matrix polynomial P (λ)∈ F [λ] n× m, n⩽ m, can be reduced to triangular form, preserving the degree and the finite and infinite elementary divisors. We also characterize the real matrix polynomials that are triangularizable over the real numbers and show that those that are not triangularizable are quasi-triangularizable with diagonal blocks of sizes 1× 1 and 2× 2. The proofs we present solve the structured inverse problem of building up triangular matrix polynomials starting from lists of elementary divisors.