Pseudo Core Inverses

Jianlong Chen and Xiaoxiang Zhang
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Jianlong Chen: Southeast University, School of Mathematics
Xiaoxiang Zhang: Southeast University, School of Mathematics

Chapter Chapter 6 in Algebraic Theory of Generalized Inverses, 2024, pp 265-314 from Springer

Abstract: Abstract For any square complex matrix A with index 1, we know that the core inverse of A exists and it is equal to A # P A # $$A^{\#}P_{A^{\#}}$$ . For a square complex matrix A of an arbitrary index, by noting that the Drazin inverse A D $$A^{D}$$ always exists, it is natural to consider the generalized inverse A D P A D $$A^{D}P_{A^{D}}$$ so as to generalize the core inverse.

Date: 2024
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DOI: 10.1007/978-981-99-8285-1_6

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