In Section 7.3 we saw that if the matrix A has n distinct (real or complex) eigenvalues with respective associated eigenvectors , then a general solution of the system
is given by
with arbitrary constants . In this section we discuss the situation when the characteristic equation
does not have n distinct roots, and thus has at least one repeated root.
An eigenvalue is of multiplicity k if it is a k-fold root of Eq. (3). For each eigenvalue , the eigenvector equation
has at least one nonzero solution v, so there is at least one eigenvector associated with . But an eigenvalue of multiplicity ...