Affiliation:
1. School of Mathematics, Southeast University, Nanjing, China
Abstract
For any complex matrices A and W, m? n and n ?m, respectively, it is proved
that there exists a complex matrix X such that AXA = A, XAX = X, (AX)* = AX
and XA(WA)k = (WA)k, where k is the index of WA. When A is square andW is
the identity matrix, such an X reduces to Greville?s spectral {1, 2,
3}-inverse of A. Various expressions of such generalized inverses are
established.
Publisher
National Library of Serbia
Reference22 articles.
1. O. M. Baksalary, G. Trenkler, Core inverse of matrices, Linear Multilinear Algebra, 58(6) (2010), 681-697.
2. O. M. Baksalary, G. Trenkler, On a generalized core inverse, Appl. Math. Comput., 236 (2014), 450-457.
3. A. Ben-Israel, T. N. E. Greville, Generalized Inverses: Theory and Applications, (2nd edition), Springer, New York, 2003.
4. S. L. Campbell, C. D. Meyer, Weak Drazin inverses, Linear Algebra Appl., 20(2) (1978), 167-178.
5. D. S. Cvetković-Ilić, Y. M. Wei, Algebraic Properties of Generalized Inverses, Springer, Singapore, 2017.