| Title | Summary |
|---|---|
| Review: Eigenvalues and Eigenvectors | Paul's On-Line Notes introducing eigenvalues and eigenvectors. |
| Linear Systems: General Solutions | Paul's On-Line Notes showing how to generate a general solution from a complete set of eigenpairs. |
| Homogeneous Linear Systems with Constant Coefficients | Professor Mattuck (MIT video) introduces eigen methods to construct a fundamental
set of solutions for a first-order homogeneous linear system with constant coefficients. In particular, he introduces eigenpairs and shows how to construct a fundamental set of solutions when there are two real eigenvalues. |
| Continuation: Repeated Real Eigenvalues, Complex Eigenvalues | Professor Mattuck (MIT video) uses eigen methods to construct a fundamental
set of solutions for a first-order homogeneous linear system with constant coefficients. In particular, he shows how to construct a fundamental set of solutions when there is either one double real eigenvalue with two indepentent eigenvectors or a conjugate pair of eigenvalues. |
| Matrix Exponentials | Professor Mattuck (MIT video) uses eigen methods to construct a fundamental set of
solutions for a first-order homogeneous linear system with constant coefficients. He then constructs the matrix exponential from the associated fundamental matrix. He defines the matrix exponential by an infinite series, whereas we defined it to be a particular fundamental matrix. He does not give a general recipe to compute the matrix exponential for any matrix. |
| Decoupling Linear Systems with Constant Coefficients | Professor Mattuck (MIT video) uses eigen methods to construct the matrix
exponential for a first-order homogeneous linear system with a constant coefficient matrix that is diagonalizable. |