i have a matrix of the form
$K=(diag(CAC^{-1}\mathbf{1}))^{-1}A$
where $C,A,K \in R^{n \times n}$, $C$ is diagonal with $c_{ii}>1$ and $\mathbf{1} \in R^{n \times 1}$ represents the vector of ones.
$A$ is a binary symmetric matrix $(a_{ij}=0,~1)$ but the diagonal elements $a_{ii}=1$, also $A=A^T$.
Can anyone help me in proving that maximum eigenvalue of $K$ is $1$ ?
The $diag(CAC^{-1}\mathbf{1})$ creates a diagonal matrix containing the row-sum of $CAC^{-1}$.