TABLE OF CONTENTS Let us consider an eigenvalue problem
| (2.1) |  |
where A is an m m real matrix, ? is an eigenvalue, and u is a corresponding eigenvector. The eigenvalues are determined from the characteristic equation
| (2.2) |  |
where I is the m m identity matrix. Since det( A ? ? I) is a polynomial of degree m with respect to ?, there are m eigenvalues, counting multiplicities. Since A is a real matrix, its eigenvalues and corresponding eigenvectors are real or appear in complex conjugate pairs. Multiplicity of an eigenvalue as a root of the characteristic equation is called algebraic multiplicity.
The eigenvalue ? is called simple if its algebraic multiplicity is equal to one. There is a single eigenvector, up to a scaling factor, corresponding to a simple eigenvalue.
