kill(all);

a general 2x2 symmetric matrix

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

solution of the eigenproblem according to a maxima internal function

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

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

ev([vals,vecs],a=1,b=2,c=3),numer;