Characterizations of EP matrices and weighted-EP matrices

Tian, Yongge; Wang, Hongxing

doi:10.1016/j.laa.2010.11.014

Cited by 42 publications

(35 citation statements)

References 34 publications

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“…For example, Tian et al. summarize thirty five characterizations of EP matrices in [29]. Theorems 2.3 and 2.4 in the present paper are related to these characterizations and Theorems 2.1 and 2.2 state conditions under which an EP matrix commutes with an arbitrary matrix.…”

Section: Introductionmentioning

confidence: 78%

The star partial order and the eigenprojection at 0 on EP matrices

Hernández

Lattanzi

Thome

et al. 2012

Applied Mathematics and Computation

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The star partial order and the eigenprojection at 0 on EPThe space of n × n complex matrices with the star partial order is considered in the first part of this paper. The class of EP matrices is analyzed and several properties related to this order are given. In addition, some information about predecessors and successors of a given EP matrix is obtained. The second part is dedicated to the study of some properties that relate the eigenprojection at 0 with the star and sharp partial orders.

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Section: Introductionmentioning

confidence: 78%

The star partial order and the eigenprojection at 0 on EP matrices

Hernández

Lattanzi

Thome

et al. 2012

Applied Mathematics and Computation

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“…The above Remark (iii), Remark 2.1 and Theorem 3.5 in [18] allow us to present some characterizations for weighted-EP matrices when M = N . Proposition 2.1 Let A ∈ C n×n .…”

Section: Remark 22mentioning

confidence: 95%

On a partial order defined by the weighted Moore–Penrose inverse

Hernández¹,

Lattanzi²,

Thome³

2013

Applied Mathematics and Computation

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“…The restricted weighted generalized inverse. For this section, we need the notion of the weighted Moore-Penrose inverse of a matrix A ∈ C m×n with respect to two Hermitian positive definite matrices M ∈ C m×m and N ∈ C n×n denoted by X = A † M,N satisfying the following four equations (see [4,page 118,Exercise 30] or [22,Section 3]; for computational methods, see [20], and for more on this subject, see [6,7]):…”

Section: Preliminaries and Notationmentioning

confidence: 99%

“…is called the V -orthogonal projector with respect to the semi-norm · V (see e.g., [21] or [22,Section 3]). The V -orthogonal projector is unique when r(V X) = r(X).…”

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confidence: 99%