Eigen Decomposition of a Square Symmetric Matrix — Eigen • matlib

Eigen calculates the eigenvalues and eigenvectors of a square, symmetric matrix using the iterated QR decomposition

Usage

Eigen(X, tol = sqrt(.Machine$double.eps), max.iter = 100, retain.zeroes = TRUE)

Arguments

X: a square symmetric matrix
tol: tolerance passed to QR
max.iter: maximum number of QR iterations
retain.zeroes: logical; retain 0 eigenvalues?

Value

a list of two elements: values– eigenvalues, vectors– eigenvectors

See also

Author

John Fox and Georges Monette

Examples

C <- matrix(c(1,2,3,2,5,6,3,6,10), 3, 3) # nonsingular, symmetric
C
#>      [,1] [,2] [,3]
#> [1,]    1    2    3
#> [2,]    2    5    6
#> [3,]    3    6   10
EC <- Eigen(C) # eigenanalysis of C
EC$vectors %*% diag(EC$values) %*% t(EC$vectors) # check
#>      [,1] [,2] [,3]
#> [1,]    1    2    3
#> [2,]    2    5    6
#> [3,]    3    6   10