XploRe Help : eisrg

Keywords - Function groups - @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Library:	math
See also:	eiscg eisrs

Quantlet:		eisrg
Description:		Computes the eigenvalues and eigenvectors of a real general matrix

Usage:	`{wr, wi, z} = eisrg(a)`
Input:
	`a`	n x n matrix
Output:
	`wr`	n x 1 vector of real eigenvalues
	`wi`	n x 1 vector of imaginary eigenvalues
	`z`	n x n matrix of eigenvectors

Note:

If the j-th eigenvalue is real, the j-th column of z contains its eigenvector. If the j-th eigenvalue is complex with positive imaginary part, the j-th and (j+1)-th columns of z contain the real and the imaginary parts of its eigenvector. The conjugate of this vector is the eigenvector for the conjugate eigenvalue.

Example:

library("math") a = #(2, -2)~#(4, 6) {wr, wi, z} = eisrg(a) wr ;real eigenvalues wi ;imaginery eigenvalues z ;eigenvectors

Result:

Contents of wr
[1,]        4
[2,]        4
Contents of wi
 [1,]        2
[2,]       -2
Contents of z
[1,]        1        1
[2,]        0        1

Author: F. Noetzel, W. Haerdle, 20010912 license MD*Tech