Schur’s theorem and the Drazin inverse

Hartwig, Robert E.

doi:10.2140/pjm.1978.78.133

Cited by 8 publications

(4 citation statements)

References 8 publications

(10 reference statements)

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“…Theorem 15. Let A ∈ C n×n with ind(A) = k and A − be a fixed inner inverse of A, both expressed as in (9). The following statements are valid.…”

Section: D Inverse and D1 Inverse Of Square Matricesmentioning

confidence: 99%

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1D inverse and D1 inverse of square matrices

Sahoo,

Maharana,

Sitha

et al. 2024

MMN

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In this paper we introduce two new classes of inverses for square matrices, which are called 1Drazin (in short, 1D) inverse and Drazin1 (in short, D1) inverse. Next, we investigated the existence and uniqueness of 1D inverse and its dual D1 inverse. Some representation and characterizations of these inverses are derived. In addition to this, we obtain some properties of 1D and D1 inverses through idempotent and binary relations.

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“…Theorem 15. Let A ∈ C n×n with ind(A) = k and A − be a fixed inner inverse of A, both expressed as in (9). The following statements are valid.…”

Section: D Inverse and D1 Inverse Of Square Matricesmentioning

confidence: 99%

“…al (1971) in [22]. The Drazin inverse in ring theory was established in [9] and the applications of Drazin inverse in solving singular linear control systems were discussed in [3]. The authors of [2,3] have pointed out the importance of Drazin inverse in matrix theory and computations.…”

Section: Introductionmentioning

confidence: 99%

1D inverse and D1 inverse of square matrices

Sahoo,

Maharana,

Sitha

et al. 2024

MMN

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“…The research on the representations of the Drazin inverse for block matrices can be seen in [16][17][18][19][20][21][22]. Many representations and computations for the Drazin inverse of a square matrix have also been widely researched [23][24][25][26][27][28][29][30][31].…”

Section: Introductionmentioning

confidence: 99%

Two methods for computing the Drazin inverse through elementary row operations

Zhang

Sheng

2016

Filomat

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In this paper, Let the matrix A ∈ C n×n with Ind(A) = k, we first construct two bordered matrices based on [32], which gave a method for computing the null space of A k by applying elementary row operations on the pair A I. Then two new Algorithms to compute the Drazin inverse A d are presented based on elementary row operations on two partitioned matrices. The computational complexities of the two Algorithms are detailed analyzed. When the index k = Ind(A) ≥ 5, the two Algorithms are all faster than the Algorithm by Anstreicher and Rothblum [32]. In the end, an example is presented to demonstrate the two new algorithms.

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“…In practice, the iterative process (2) is very expensive. It motivates us to construct a new iteration whose quantity of matrix multiplications at each step is less than that of (2) and whose error bound is between (3) and (4). In addition, the restriction of the initial value is relaxed.…”

Section: Introductionmentioning

confidence: 99%