Finding spectral radius of matrix without computing characteristic polynomial

linear-algebra matrices eigenvalues-eigenvectors numerical-linear-algebra spectral-radius

Solution 1:

I found a solution, I post it in order to mark the question as answered.

As shown here, since $\sum_{i=1}^3a_{ij}=4$ for $j=1,2,3$, we have that 4 is eigenvalue of $A$. Therefore, $$\rho(A)\geq4$$ and we conclude $\rho(A)=4$.

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