MatMPpinv {mixAK}R Documentation

Moore-Penrose pseudoinverse of a squared matrix

Description

For a matrix A its Moore-Penrose pseudoinverse is such a matrix A[+] which satisfies
(i) A*A[+]*A = A,
(ii) A[+]*A*A[+] = A[+],
(iii) (A*A[+])' = A*A[+],
(iv) (A[+]*A)' = A[+]*A.
Computation is done using spectral decomposition. At this moment, it is implemented for symmetric matrices only.

Usage

  MatMPpinv(A)

Arguments

A either a numeric vector in which case inverse of each element of A is returned or a squared matrix.

Value

Either a numeric vector or a matrix.

Author(s)

Arnošt Komárek arnost.komarek[AT]mff.cuni.cz

References

Golub, G. H. and Van Loan, C. F. (1996, Sec. 5.5). Matrix Computations. Third Edition. Baltimore: The Johns Hopkins University Press.

Examples

set.seed(770328)
A <- rWishart(1, 5, diag(4))
Ainv <- MatMPpinv(A)

### Check the conditions
prec <- 13
round(A - A %*% Ainv %*% A, prec)
round(Ainv - Ainv %*% A %*% Ainv, prec)
round(A %*% Ainv - t(A %*% Ainv), prec)
round(Ainv %*% A - t(Ainv %*% A), prec)

[Package mixAK version 0.6 Index]