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Campbell, S.L. and Meyer, C.D. (1979) Generalized Inverses of Linear Transformations. Dover Publ, New York.

has been cited by the following article:

• TITLE: Moore-Penrose Inverse and Semilinear Equations

  AUTHORS: Hugo Leiva, Raúl Manzanilla

  KEYWORDS: Semilinear Equations, Moore-Penrose Inverse, Rothe’s Fixed Point Theorem

  JOURNAL NAME: Advances in Linear Algebra & Matrix Theory, Vol.8 No.1, January 17, 2018

  ABSTRACT: In this paper, we study the existence of solutions for the semilinear equation , where A is a , , and is a nonlinear continuous function. Assuming that the Moore-Penrose inverse AT(AAT)-1exists (A denotes the transposed matrix of A) which is true whenever the determinant of the matrix AAT is different than zero, and the following condition on the nonlinear term satisfied . We prove that the semilinear equation has solutions for all. Moreover, these solutions can be found from the following fixed point relation .