Repeated Eigenvalues

• cours magistral
• cours magistral - matière potentielle : differential equations

Differential Equations LECTURE 34 Repeated Eigenvalues The final case we need to consider involves repeated eigenvalues. In the previous two cases, we had distinct eigenvalues, which, as Theorem 31.3 a few lectures ago told us, have linearly independent eigenvectors. Thus, all we had to do was to calculate those eigenvectors and write down solutions of the form xi(t) = η(i)eλit. In the real case, the linear independence of the eigenvectors and the differing eigenvectors assured us that these two solutions formed a fundamental set, and so our general solution was just a linear combination of the two.

• eigenvector of the coefficient matrix
• eigensolution
• general solution to the following system
• origin parallel to the eigensolution
• basic fact from linear algebra
• eigenvalue
• linear combination
• differential equations
• origin
• solution