The Moore--Penrose Generalized Inverse for Sums of Matrices

The Moore-Penrose Generalized Inverse for Sums of Matrices

In this paper we exhibit, under suitable conditions, a neat relationship between the Moore–Penrose generalized inverse of a sum of two matrices and the Moore–Penrose generalized inverses of the individual terms. We include an application to the parallel sum of matrices. AMS 1991 subject classifications. Primary 15A09; secondary 15A18.

Fast Computation of Moore-Penrose Inverse Matrices

Many neural learning algorithms require to solve large least square systems in order to obtain synaptic weights. Moore-Penrose inverse matrices allow for solving such systems, even with rank deficiency, and they provide minimum-norm vectors of synaptic weights, which contribute to the regularization of the input-output mapping. It is thus of interest to develop fast and accurate algorithms for ...

The Moore-Penrose Inverse of Intuitionistic Fuzzy Matrices

In this paper, we define the various g-inverses of an intuitionistic fuzzy matrices, left (right ) cancelable intuitionistic fuzzy matrices and derive the equivalent condition for the existence of the generalized inverses . We also study the relation between the minus-ordering and the various g–inverses of an intuitionistic fuzzy matrix.

New representations for the Moore-Penrose inverse

Minors of the Moore - Penrose Inverse ∗

Let Qk,n = {α = (α1, · · · , αk) : 1 ≤ α1 < · · · < αk ≤ n} denote the strictly increasing sequences of k elements from 1, . . . , n. For α, β ∈ Qk,n we denote by A[α, β] the submatrix of A with rows indexed by α, columns by β. The submatrix obtained by deleting the α-rows and β-columns is denoted by A[α′, β′]. For nonsingular A ∈ IRn×n, the Jacobi identity relates the minors of the inverse A−1...