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Journals / European Journal of Pure and Applied Mathematics (elektronik) / 2012 / Cilt: 5 - Sayı: 4

The Drazin inverses of combinations of two idempotents

Tao XIE
Kezheng ZUO
Pages
480–491
Publication Date
2022-10-18
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

These generalized the related results of Deng’s work, which characterized the Drazin inverse of the sum and difference of two idempotents. 2010 Mathematics Subject Classifications: 15A09, 47A05

📌 3 Key Takeaways

🎯
Objective & Hypothesis:By using the methods of splitting operator’s matrix into blocks and space decompositions, the existence and calculation formulas of Drazin inverse of the combinations aP + bQ+cPQ+dQP of two idempotent operators P and Q on a Hilbert space are obtained under the conditions PQP = 0, PQP = P and PQP = PQ respectively.
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Key Findings & Data:By using the methods of splitting operator’s matrix into blocks and space decompositions, the existence and calculation formulas of Drazin inverse of the combinations aP + bQ+cPQ+dQP of two idempotent operators P and Q on a Hilbert space are obtained under the conditions PQP = 0, PQP = P and PQP = PQ respectively.
💡
Conclusion & Impact:These generalized the related results of Deng’s work, which characterized the Drazin inverse of the sum and difference of two idempotents. 2010 Mathematics Subject Classifications: 15A09, 47A05
🔬Design:Research Article
📍Scope:2010 Verileri
⚙️Variables:Domain Parameters

Abstract

By using the methods of splitting operator’s matrix into blocks and space decompositions, the existence and calculation formulas of Drazin inverse of the combinations aP + bQ+cPQ+dQP of two idempotent operators P and Q on a Hilbert space are obtained under the conditions PQP = 0, PQP = P and PQP = PQ respectively. These generalized the related results of Deng’s work, which characterized the Drazin inverse of the sum and difference of two idempotents. 2010 Mathematics Subject Classifications: 15A09, 47A05

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Cite This Article

XIE, T., ZUO, K. (2022). The Drazin inverses of combinations of two idempotents. European Journal of Pure and Applied Mathematics (elektronik), Cilt: 5 - Sayı: 4, 480–491. https://ajindex.com/articles/511254

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