Symbolic Math Toolbox™

eig - Symbolic eigenvalues and eigenvectors

Syntax

lambda = eig(A) [V,D] = eig(A) [V,D,P] = eig(A) lambda = eig(vpa(A)) [V,D] = eig(vpa(A))

Description

lambda = eig(A) returns a symbolic vector containing the eigenvalues of the square symbolic matrix A.

[V,D] = eig(A) returns a matrix V whose columns are eigenvectors and a diagonal matrix D containing eigenvalues. If the resulting V is the same size as A, then A has a full set of linearly independent eigenvectors that satisfy A*V = V*D.

[V,D,P] = eig(A) also returns P, a vector of indices whose length is the total number of linearly independent eigenvectors, so that A*V = V*D(P,P).

lambda = eig(vpa(A)) and [V,D] = eig(vpa(A)) compute numeric eigenvalues and eigenvectors, respectively, using variable precision arithmetic. If A does not have a full set of eigenvectors, the columns of V will not be linearly independent.

Examples

The statements

R = sym(rosser);
eig(R)

return

ans =
[                0]
[             1020]
[ 510+100*26^(1/2)]
[ 510-100*26^(1/2)]
[   10*10405^(1/2)]
[  -10*10405^(1/2)]
[             1000]
[             1000]

eig(vpa(R)) returns

ans =

[    -1020.0490184299968238463137913055]
[ .56512999999999999999999999999800e-28]
[  .98048640721516997177589097485157e-1]
[     1000.0000000000000000000000000002]
[     1000.0000000000000000000000000003]
[     1019.9019513592784830028224109024]
[     1020.0000000000000000000000000003]
[     1020.0490184299968238463137913055]