About the group inverse and Moore-Penrose inverse of a product

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...

About the generalized LM-inverse and the weighted Moore-Penrose inverse

The recursive method for computing the generalized LM inverse of a constant rectangular matrix augmented by a column vector is proposed in [16, 17]. The corresponding algorithm for the sequential determination of the generalized LM -inverse is established in the present paper. We prove that the introduced algorithm for computing the generalized LM inverse and the algorithm for the computation o...

When Does the Moore–penrose Inverse Flip?

In this paper, we give necessary and sufficient conditions for the matrix [ a 0 b d ] , over a *-regular ring, to have a Moore-Penrose inverse of four different types, corresponding to the four cases where the zero element can stand. In particular, we study the case where the MoorePenrose inverse of the matrix flips. Mathematics subject classification (2010): 15A09, 16E50, 16W10.

New representations for the Moore-Penrose inverse

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 ...