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Results tagged with eigenvalues
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user 141956
eigenvalues of matrices or operators
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Sum of eigenvalues is nonpositive
How can I show that the sum of the largest $n-k+1$ eigenvalues of $A - k\cdot \textrm{diag}(A)$ is nonpositive, for any $k \in \{1, \dots, n\}$? … When $m = n/k$ this means $\lambda_{n/k} \le 0$, which is not hard to show by looking at the eigenvalues of $D^{-1/2} A D^{-1/2}$ where $D = \textrm{diag}(A)$. …
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