The quasi-Weierstra脽 form for regular matrix pencils

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• 作者：Thomas Berger^a ; ^{thomas.berger@tu-ilmenau.de} ; Achim Ilchmann^a ; ^{achim.ilchmann@tu-ilmenau.de} ; Stephan Trenn^b ; ^{trenn@illinois.edu}
• 关键词：Linear matrix pencils ; Differential algebraic equations ; Generalized eigenspaces ; Weierstraß ; form ; Quasi-Weierstraß ; form
• 刊名：Linear Algebra and its Applications
• 出版年：2012
• 期刊代码：38_00243795
• 类别：mt
• 出版时间：15 May, 2012
• 卷：436
• 期：10
• 页码：4052-4069
• 文件大小：292 K

摘要

Regular linear matrix pencils , where , or , and the associated differential algebraic equation (DAE) are studied. The Wong sequences of subspaces are investigate and invoked to decompose the into , where any bases of the linear spaces and transform the matrix pencil into the quasi-Weierstra脽 form. The quasi-Weierstra脽 form of the matrix pencil decouples the original DAE into the underlying ODE and the pure DAE or, in other words, decouples the set of initial values into the set of consistent initial values and 鈥減ure鈥?inconsistent initial values . Furthermore, and are spanned by the generalized eigenvectors at the finite and infinite eigenvalues, resp. The quasi-Weierstra脽 form is used to show how chains of generalized eigenvectors at finite and infinite eigenvalues of lead to the well-known Weierstra脽 form. So the latter can be viewed as a generalized Jordan form. Finally, it is shown how eigenvector chains constitute a basis for the solution space of .