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Results tagged with block-matrices
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user 13650
7
votes
How to prove this determinant is positive?
Here is a counterexample with $N=3$. Consider the matrices
$$ B_1 = \log(t) \pmatrix{0 & 4\cr -1 & 0\cr}, B_2 = \log(t) \pmatrix{-2 & 2\cr 1 & 2\cr}, B_3 = \log(t) \pmatrix{4 & -2\cr -2 & 1\cr}$$
whe …
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4
votes
Accepted
Spectrum of this block matrix
If $\lambda_\max$ is the greatest eigenvalue of $T$, the least eigenvalue of $A$ is between $-\lambda_\max$ and $\max(b_1, b_n) - \lambda_\max$.
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