eig (Symbolic Math Toolbox)

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Symbolic matrix 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(gallery('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]

The statements

A = sym(gallery(5));
[v,lambda] = eig(A)

return

v =
[       0]
[  21/256]
[ -71/128]
[ 973/256]
[       1]

lambda =
 
[ 0, 0, 0, 0, 0]
[ 0, 0, 0, 0, 0]
[ 0, 0, 0, 0, 0]
[ 0, 0, 0, 0, 0]
[ 0, 0, 0, 0, 0]