nlr (version 0.1-3)

eiginv: Inverse of matrix using eigenvalues.

Description

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

Usage

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

Arguments

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.

Value

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.

Details

eiginv function compute the inverse of matrix using spectoral decomposition $$ A_{k \times k}=\textbf{P} \Lambda \textbf{P}' $$ where $$ \textbf{P}=[e_1,\dots,e_k] $$ $$ \Lambda=diag(\lambda_i) $$ in which \(\lambda_i\) is eigenvalues of matrix A coresponding to eigenvector \(e_i\). Then the inverse is: $$ A^{-1}=\textbf{P} \Lambda^{-1} \textbf{P}' $$

References

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

See Also

indifinv

Examples

# NOT RUN {
 a1=matrix(c(1,2,3,4,5,6,7,8,9),nrow=3)
eiginv(a1)
# }