- #1

- 159

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(A - λI)x

_{k+1}= x

_{k}, where A is a square matrix, x is an eigenvector, λ is the eigenvalue I is the identity matrix.

This might be used, for example, if we have duplicate eigenvalues, and can only derive one eigenvector from the characteristic equation, then we can use this eigenvector to find other eigenvectors.

Can someone explain this formula? I don't really get it. My textbook has a similar formula:

x

_{k+1}= Ax

_{k}

which I understand perfectly. But how does the former formula make sense?