Kernel structure of Toeplitz-plus-Hankel matrices

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• 作者：Heinig ; Georg
• 关键词：Toeplitz matrix ; Toeplitz-plus-Hankel matrix
• 刊名：Linear Algebra and its Applications
• 出版年：2002
• 期刊代码：38_00243795
• 类别：mt
• 出版时间：January 1, 2002
• 卷：340
• 期：1-3
• 页码：1-13
• 文件大小：120 K

摘要

The structure of the kernel of block Toeplitz-plus-Hankel matrices R=[a_j−k+b_j+k], where a_j and b_j are the given p×q blocks with entries from a given field, is investigated. It is shown that R corresponds to two systems of at most p+q vector polynomials from which a basis of the kernel of R and all other Toeplitz-plus-Hankel matrices with the same parameters a_j and b_j can be built. The main result is an analogue of a known kernel structure theorem for block Toeplitz and block Hankel matrices.