Jordan normal form
If we are given an "n" × "n" matrix formula_2 and wish to find a matrix formula_56 in Jordan normal form, similar to formula_2, we are interested only in sets of linearly independent generalized eigenvectors. A matrix in Jordan normal form is an "almost diagonal matrix," that is, as close to diagonal as possible. A diagonal matrix formula_58 is a special case of a matrix in Jordan normal form. An ordinary eigenvector is a special case of a generalized eigenvector.