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Results tagged with perturbation
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user 11260
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vote
Robust generalization of matrix rank
The rank of a fuzzy matrix and its evaluation
A new type of matrix rank, which is called margin rank in this
article, is introduced to a fuzzy matrix defined to be rectangular
array of fuzzy n …
- 188k
1
vote
Separating the spectrum of a Hermitian matrix
adding a nonzero $A$ will not change much; the degenerate eigenvalues of $A$ will split by an amount of order $\epsilon$ as a result of the perturbation by $\epsilon G$, which is already much larger than …
- 188k
2
votes
Accepted
Distribution of the spectrum of a perturbed matrix
Since $P(G)\propto{\rm exp}\bigl(-\frac{1}{2}{\rm Tr}\,GG^{\rm T}\bigr)$ is invariant under orthogonal transformations, if $A$ is real Hermitian you can work in a basis where $A$ is diagonal, with the …
- 188k