首页|The {1, 2, 3, 1(m)}-inverses: A generalization of core inverses for matrices
The {1, 2, 3, 1(m)}-inverses: A generalization of core inverses for matrices
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NSTL
Elsevier
This paper concerns a new generalized inverse for matrices of an arbitrary index. It is proved that every complex square matrix A possesses a {1 , 2 , 3}-inverse X such that XA(m+1) = A(m) for some integer m . We shall call such X a { 1 , 2 , 3 , 1 m }-inverse of A . A notable result is that A has a unique {1 , 2 , 3 , 1(m)}-inverse if and only if it has index 0 or 1, in which case A* is exactly its unique {1 , 2 , 3 , 1 (m)}-inverse. For a matrix with an arbitrary index, the set of all its {1 , 2 , 3 , 1(m)}-inverses is completely determined. Some new characterizations of EP matrices, generalized EP matrices and m-EP matrices are established by using their {1 , 2 , 3 , 1(m)}-inverses. (C) 2022 Elsevier Inc. All rights reserved.
NSTL
Elsevier
