1
$\begingroup$

Let $A$ be a matrix with real eigenvalues, its maximum eigenvalue is $0$ and it has sum for rows equals to zero. Let $B$ be a matrix $\mathrm{diag}([1\,0\, ...\, 0])$ and let $I$ be the identity matrix. Then $\lambda_{\max}(A+B)\neq\lambda_{\max}(A+I)=1$ ?

The last equality is from $\lambda(A+I)=\lambda(A)+1$.

$\endgroup$
2
  • $\begingroup$ I have tried with a generic diagonal matrix $B=\begin{bmatrix}I & 0\\0&0 \end{bmatrix}$ $\endgroup$
    – Thomas
    Mar 4, 2014 at 11:01
  • $\begingroup$ A is negative semi definite matrix.. $\endgroup$
    – Thomas
    Mar 4, 2014 at 11:07

0

Reset to default

You must log in to answer this question.