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Results tagged with eigenvalues
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user 141429
eigenvalues of matrices or operators
1
vote
2
answers
519
views
How to find bounds on the eigenvalues of a matrix?
Given this matrix
$M=\begin{bmatrix} 0 & m-1 & 2 & n-1\\
1 & m-2& 1 & n-1\\
2 & m-1 & 0 & 2(n-1)\\
1 & m-1 & 2 & 2(n-2)\end{bmatrix},$ show that if $\alpha_1,\alpha_2$ are two negative eigenvalues of $ … Does there exist any theorem/trick to find a better upper bound of the sum of two negative eigenvalues of a matrix?
If someone can help, I will be grateful. …
- 444
9
votes
3
answers
3k
views
What happens to eigenvalues when edges are removed?
Let the eigenvalues of $A$ be $\lambda_1\le \lambda_2\leq \cdots \leq \lambda_n$. … I know Cauchy Interlacing Theorem which gives the relation between eigenvalues of a graph and its induced subgraph when some vertices are removed. …
- 444