eiginv: Inverse of matrix using eigenvalues.
In nlr: Nonlinear Regression Modelling using Robust Methods

Description Usage Arguments Details Value Note Author(s) References See Also Examples

Compute the inverse of matrix using spectoral decomposition, using eigenvalues and eigen vectors of matrix.

1	eiginv(mtrx, stp = T, symmetric = all(mtrx == t(mtrx)))

`mtrx`	square matrix to compute the inverse.
`stp`	if stp=T when error happened stop running program, if stp=F, does not stop program but return back Fault object.
`symmetric`	Used for computing eigenvalues, if symmetric=T the matrix is symetric, if symmetric=F the matrix is not symetric.

eiginv function compute the inverse of matrix using spectoral decomposition

A_{k \times k}=\textbf{P} Λ \textbf{P}'

where

\textbf{P}=[e_1,…,e_k]

Λ=diag(λ_i)

in which λ_i is eigenvalues of matrix A coresponding to eigenvector e_i. Then the inverse is:

A^{-1}=\textbf{P} Λ^{-1} \textbf{P}'

If matrix is positive definit, that is all eigenvalues are positive, return the inverse of matrix, if matrix is not positive definit returns Fault object with fault number=9, means the matrix is not positive definit.

This function mostly used in optimization subroutindes, thus the inverse of negative definit matrix returned as fault. In contrast the indifinv function return back the same inverse eventhough the matrix is not positive definit.

Hossein Riazoshams, Jan 2010. Email: riazihosein@gmail.com URL http://www.riazoshams.com/nlr/

Riazoshams H, Midi H, and Ghilagaber G, 2018,. Robust Nonlinear Regression, with Application using R, Joh Wiley and Sons.

indifinv