Eigen Decomposition of a Square Symmetric Matrix

Source: R/Eigen.R

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

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

eigen

SVD

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