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Maple can compute exact formulae for eigenvalues and eigenvectors
as well as numerical approximations. E.g. given the matrix
> A := matrix( 3,3, [sqrt(2),x,alpha,x,sqrt(2),x,alpha,x,sqrt(2)] );
The eigenvalues are the roots of the characteristic polynomial
> factor(charpoly(A,lambda));
Note that Maple has factored the characteristic polynomial over
. Solving for 
we obtain
> e := eigenvals(A);
For each eigenvalue 
, a basis for its corresponding eigenvectors
is given by the nullspace of characteristic matrix 
, i.e.
> seq( nullspace(charmat(A,lambda)), lambda = e );
