The DMP inverse for rectangular matrices

Filomat ◽  
2017 ◽  
Vol 31 (19) ◽  
pp. 6015-6019 ◽  
Author(s):  
Lingsheng Meng
Keyword(s):  
Drazin Inverse ◽  
Definition Of ◽  
Weighted Drazin Inverse ◽  
Square Matrix

The definition of the DMP inverse of a square matrix with complex elements is extended to rectangular matrices by showing that for any A and W, m by n and n by m, respectively, there exists a unique matrix X, such that XAX = X, XA = Wad, wWA and (WA)k+1X =(WA)k+1A+, where Ad,w denotes the W-weighted Drazin inverse of A and k = Ind(AW), the index of AW.

Recurrent neural network for computing the W -weighted Drazin inverse

2017 ◽  
Vol 300 ◽  
pp. 1-20 ◽  
Author(s):  
Xue-Zhong Wang ◽  
Haifeng Ma ◽  
Predrag S. Stanimirović
Keyword(s):  
Neural Network ◽  
Recurrent Neural Network ◽  
Drazin Inverse ◽  
Weighted Drazin Inverse

Characterizations for the n-strong Drazin invertibility in a ring

2020 ◽  
pp. 2150141
Author(s):  
Honglin Zou ◽  
Jianlong Chen ◽  
Huihui Zhu ◽  
Yujie Wei
Keyword(s):  
Positive Integer ◽  
Generalized Inverse ◽  
Product Formula ◽  
Drazin Inverse ◽  
Equivalent Definition ◽  
New Type ◽  
Definition Of ◽  
Existence Criteria

Recently, a new type of generalized inverse called the [Formula: see text]-strong Drazin inverse was introduced by Mosić in the setting of rings. Namely, let [Formula: see text] be a ring and [Formula: see text] be a positive integer, an element [Formula: see text] is called the [Formula: see text]-strong Drazin inverse of [Formula: see text] if it satisfies [Formula: see text], [Formula: see text] and [Formula: see text]. The main aim of this paper is to consider some equivalent characterizations for the [Formula: see text]-strong Drazin invertibility in a ring. Firstly, we give an equivalent definition of the [Formula: see text]-strong Drazin inverse, that is, [Formula: see text] is the [Formula: see text]-strong Drazin inverse of [Formula: see text] if and only if [Formula: see text], [Formula: see text] and [Formula: see text]. Also, we obtain some existence criteria for this inverse by means of idempotents. In particular, the [Formula: see text]-strong Drazin invertibility of the product [Formula: see text] are investigated, where [Formula: see text] is regular and [Formula: see text] are arbitrary elements in a ring.

Condition number of the W-weighted Drazin inverse

2008 ◽  
Vol 203 (1) ◽  
pp. 308-318 ◽  
Author(s):  
Dijana Mosić ◽  
Dragan S. Djordjević
Keyword(s):  
Condition Number ◽  
Drazin Inverse ◽  
Weighted Drazin Inverse
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