Matrix Partial Orders, Shorted Operators and Applications

By S. Mitra, P. Bhimasankaram, S. Malik. 2010

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On a new generalized inverse of matrices (2018, unknown): “Formore information about these inverses see [1,2].”
Weak group inverse (2017, methodology): “f A and A# = U T−1 0 0 0 U∗, (2.3) A# = U T−1 T−2S 0 0 U∗, (2.4) 30 where T = ΣK and S = ΣL. It is well known that the core-nilpotent decomposition has been widely used in matrix theory [3, 8, 13]: 3 LEMMA 2.3. [13, Core-nilpotent decomposition] Let A ∈ C n,n be with Ind(A) = k, then A can be ”
The gDMP inverse of Hilbert space operators (2018, unknown): “The generalized Drazin pre-order as an extension of Drazin order for complex matrices [11], and it was deﬁned In [13], the core-EP inverse is introduced for a square matrix over an arbitrary ﬁeld which.”