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Generalized n-idempotents and Hyper-generalized n-idempotents
TLDR
In this paper, a chain of proper inclusions of all n-idempotents, all generalized nidempotent, and all hyper-generalized n-empotents is obtained.Abstract:
For an integer n≥2,we say that an operator A is an n-idempotent if A~n=A;A is a generalized n-idempotent if A~n=A~*;A is a hyper-generalized n- iclempotent if A~n=A~+.The set of all n-idempotents,all generalized n-idempotents and all hyper-generalized n-idempotents are denoted by I_n(H),GI_n(H)and HGI_n(H),respectively.In this note,we obtain a chain of proper inclusions GI_n(H)HGI_n(H)I_(n+2)(H).read more
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Nonsingularity and group invertibility of linear combinations of two k-potent matrices
TL;DR: In this article, the range space, null space, nonsingularity and group invertibility of linear combinations T = c 1 T 1 + c 2 T 2 of two k-potent matrices T 1 and T 2 were studied.
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On invertibility of combinations of k-potent operators
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Properties of the combinations of commutative idempotents
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The Group Inverse of the Combinations of Two Idempotent Operators
Shunqin Wang,Chunyuan Deng +1 more
TL;DR: In this article, the authors present some inverses for linear combinations of two idempotents and their products and show that the group-inverses result holds for both linear combinations and linear combinations.
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Characterizations and the Moore-Penrose inverse of hypergeneralized k-projectors
TL;DR: In this paper, the Moore-Penrose inverse of a linear combination of hypergeneralized k-projectors is found and the invertibility for some linear combinations of commuting hyper-generalizedk-projector is considered.