Convex-Cyclic Matrices, Convex-Polynomial Interpolation & Invariant Convex Sets
Convex-Cyclic Matrices, Convex-Polynomial Interpolation & Invariant Convex Sets
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DOI：
10.7153/oam-2017-11-31
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发表时间：
2015-07
期刊：
影响因子：
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通讯作者：
N. Feldman;Paul J. McGuire
中科院分区：
文献类型：
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作者：
N. Feldman;Paul J. McGuire
我们定义一个凸多项式是一个是一个凸组合的单项式$\{1，z，z^2，\ldots\}$。本文探讨了峰化凸多项式、内插凸多项式、不变凸集与矩阵动力学之间的密切联系。特别是，我们使用这些交织的关系，既证明哪些矩阵是凸循环的，而在同一时间证明，我们可以规定的值和有限数量的衍生物的凸多项式受到某些自然的约束。这些性质也等价于确定那些不变闭凸集都是不变子空间的矩阵。我们的凸循环矩阵的特征给出了一个新的和正确的证明类似的结果Rezaei是陈述和证明不正确。
We define a convex-polynomial to be one that is a convex combination of the monomials $\{1, z, z^2, \ldots\}$. This paper explores the intimate connection between peaking convex-polynomials, interpolating convex-polynomials, invariant convex sets, and the dynamics of matrices. In particular, we use these intertwined relations to both prove which matrices are convex-cyclic while at the same time proving that we can prescribe the values and a finite number of the derivatives of a convex-polynomial subject to certain natural constraints. These properties are also equivalent to determining those matrices whose invariant closed convex sets are all invariant subspaces. Our characterization of the convex-cyclic matrices gives a new and correct proof of a similar result by Rezaei that was stated and proven incorrectly.