On the covariance of 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...

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

Spectral analysis of the Moore-Penrose inverse of a large dimensional sample covariance matrix

For a sample of n independent identically distributed p-dimensional centered random vectors with covariance matrix Σn let S̃n denote the usual sample covariance (centered by the mean) and Sn the non-centered sample covariance matrix (i.e. the matrix of second moment estimates), where p > n. In this paper, we provide the limiting spectral distribution and central limit theorem for linear spectral...

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 ...