Eigen: Eigen Decomposition of a Square Symmetric Matrix

In matlib: Matrix Functions for Teaching and Learning Linear Algebra and Multivariate Statistics

Eigen Decomposition of a Square Symmetric Matrix

Description

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

Author(s)

John Fox and Georges Monette

See Also

eigen

SVD

Examples

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

matlib documentation built on Oct. 3, 2024, 1:09 a.m.