Additive and multiplicative perturbation bounds for the Moore-Penrose inverse

The optimal perturbation bounds for the weighted Moore-Penrose inverse

In this paper, we obtain optimal perturbation bounds of the weighted Moore-Penrose inverse under the weighted unitary invariant norm, the weighted Q-norm and the weighted F -norm, and thereby extend some recent results.

Ela the Optimal Perturbation Bounds for the Weighted Moore-penrose Inverse

In this paper, we obtain optimal perturbation bounds of the weighted Moore-Penrose inverse under the weighted unitary invariant norm, the weighted Q-norm and the weighted F -norm, and thereby extend some recent results.

New representations for the Moore-Penrose inverse

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.

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...