I am reading Boyd's Convex Optimization text, and I am looking at a relation between the trace and the eigenvalue of a matrix. It is on page 92, example 3.23, line 7.
The matrix $Y$ (apparently) has only one eigenvector $v$, $v^T v = 1$, and it (apparently) has only one eigenvalue $\lambda$. Also, $Y$ is not positive semidefinite, nor is it positive definite.
$$ tr(Y v v^T) = \lambda$$
Why is this so? I know the trace is equal to the sum of the eigenvalues.