A class of Hessenberg matrices with known pseudoinverse and Drazin inverse
نویسندگان
چکیده
منابع مشابه
A Class of Hessenberg Matrices with Known Pseudoinverse and Drazin Inverse
In this paper, a class of Hessenberg matrices is presented for adoption as test matrices. The Moore-Penrose inverse and the Drazin inverse for each member of this class are determined explicitly.
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There is proposed a representation of the Drazin inverse of a given polynomial square matrix, based on the extension of the Leverrier-Faddeev algorithm. Also, an algorithm for symbolic computation of the Drazin inverse of polynomial matrix is established. This algorithm represents an extension of the papers [5], [7] and a continuation of the papers [8], [9], [10]. The implementation is develope...
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Given a singular square matrix A with index r, ind(A) = r, we establish several characterizations in the Drazin inverse framework of the class of matrices B, which satisfy the conditions N (Bs)∩R(Ar) = {0} and R(Bs)∩N (Ar) = {0} with ind(B) = s, where N (A) and R(A) denote the null space and the range space of a matrix A, respectively. We give explicit representations for BD and BBD and upper b...
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Let H ∈ Cn×n be an n × n unitary upper Hessenberg matrix whose subdiagonal elements are all positive. Partition H as H = H11 H12 H21 H22 , (0.1) where H11 is its k×k leading principal submatrix; H22 is the complementary matrix of H11. In this paper, H is constructed uniquely when its eigenvalues and the eigenvalues of b H11 and b H22 are known. Here b H11 and b H22 are rank-one modifications of...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1975
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-1975-0368407-2