kill(all);

a general 2x2 symmetric matrix

M : matrix([a,b],[b,c]);

solution of the eigenproblem according to a maxima internal function

[[vals,vmult],vecs]:eigenvectors(M);

an eigenvalue list

vals;

the associated multiplicity

vmult;

the eigenvectors; the expression is corrected to avoid the avoidable eigenvector singularity for b=0

vecs:vecs*2*b;

numerical results in a specific case, for comparison

defM:[a=1,b=2,c=3];

ev([vals,vecs],defM),numer;

numerical evaluation based on lapack subroutines

/*loads the lapack library interface (it also compiles it if necessary)*/
load(lapack); 

/*calls the "dgeev" lapack subroutine to extract the eigenvalues, and optionally the right and the left eigenvectors*/
[L, v, u] : dgeev (ev(M,defM), true, true); 