کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
9507137 1631841 2005 31 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Function of a square matrix with repeated eigenvalues
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
Function of a square matrix with repeated eigenvalues
چکیده انگلیسی
An analytical function f(A) of an arbitrary n×n constant matrix A is determined and expressed by the “fundamental formula”, the linear combination of constituent matrices. The constituent matrices Zkh, which depend on A but not on the function f(s), are computed from the given matrix A, that may have repeated eigenvalues. The associated companion matrix C and Jordan matrix J are then expressed when all the eigenvalues with multiplicities are known. Several other related matrices, such as Vandermonde matrix V, modal matrix W, Krylov matrix K and their inverses, are also derived and depicted as in a 2-D or 3-D mapping diagram. The constituent matrices Zkh of A are thus obtained by these matrices through similarity matrix transformations. Alternatively, efficient and direct approaches for Zkh can be found by the linear combination of matrices, that may be further simplified by writing them in “super column matrix” forms. Finally, a typical example is provided to show the merit of several approaches for the constituent matrices of a given matrix A.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied Mathematics and Computation - Volume 160, Issue 3, 27 January 2005, Pages 819-849
نویسندگان
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