On polynomial identities of Jordan pairs of rectangular matrices
نویسندگان
چکیده
منابع مشابه
Computing Popov and Hermite forms of rectangular polynomial matrices
We consider the computation of two normal forms for matrices over the univariate polynomials: the Popov form and the Hermite form. For matrices which are square and nonsingular, deterministic algorithms with satisfactory cost bounds are known. Here, we present deterministic, fast algorithms for rectangular input matrices. The obtained cost bound for the Popov form matches the previous best know...
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Given a (k+1)-tuple A,B1, . . . , Bk of (m×n)-matrices withm ≤ n we call the set of all k-tuples of complex numbers {λ1, . . . , λk} such that the linear combination A + λ1B1 + λ2B2 + . . . + λkBk has rank smaller than m the eigenvalue locus of the latter pencil. Motivated primarily by applications to multi-parameter generalizations of the Heine-Stieltjes spectral problem, see [He] and [Vol], w...
متن کاملOn Eigenvalues of Rectangular Matrices
Given a (k+1)-tuple A,B1, . . . , Bk of (m×n)-matrices withm ≤ n we call the set of all k-tuples of complex numbers {λ1, . . . , λk} such that the linear combination A + λ1B1 + λ2B2 + . . . + λkBk has rank smaller than m the eigenvalue locus of the latter pencil. Motivated primarily by applications to multi-parameter generalizations of the Heine-Stieltjes spectral problem, see [He] and [Vol], w...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1997
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(97)80013-4