Eigenvalue solution methods

As we discussed in Chapter 1, any matrix A has eigenvalues, λj, and corresponding eigenvectors xj, as expressed in the following standard eigenvalue problem:

Ax xj j j, j 1, , n= =λ  (7.1)

The above system of equations can also be written in the following form:

( )A I x− =λ 0(7.2)

For this equation to have a nonzero solution vector x, the determinant of its matrix must be zero. This leads to an nth degree polynomial in the variable λ.