# Eigenvalue and and eigenvector

1. Jun 5, 2014

### Gianfelici

Hi, I have a problem with the calculation of the eigenvalue of a matrix. That matrix is an N x N matrix which can be written as:

$M^{ab} = A\delta^{ab} + B \phi^a \phi^b$

where $\delta^{ab}$ is the identity matrix and the $\phi$ is a column vector. The paper I'm studying says that the eigenvalue of this matrix are:

A with molteplicity 1

$A + \phi^2 B$ with molteplicity N-1

but I can't understand why! Can anyone help me?

Last edited: Jun 5, 2014
2. Jun 5, 2014