The coefficients for the principal components are unique (except for a change in sign) if the eigenvalues are distinct and not zero. If an eigenvalue is repeated, then the "space spanned" by all the principal component vectors corresponding to the same eigenvalue is unique, but the individual vectors are not. Therefore, the coefficients that Minitab displays in output and those in a book or another program may not agree, although the eigenvalues (variances of the components) will always be the same.
If the covariance matrix has rank r < p, where p is the number of variables, then there will be p – r eigenvalues equal to zero. Eigenvectors corresponding to these eigenvalues may not be unique. This can happen if the number of observations is less than p or if there is multicollinearity.