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Results tagged with perturbation-theory
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user 90413
2
votes
Accepted
Finding $\theta$ such that at least one eigenvalue of $A(\theta)$ is real
Let $A(\theta)$ be a real $n\times n$ matrix. If $n$ is odd, there must be at least one real eigenvalue due to complex conjugate pairs, see the argument of @Carlo.
If $n$ is even, you can discuss the …
- 3,736
3
votes
How do I solve the following definite integral (preferably by an asymptotic method)?
I really like the double-series approach by @AccidentalFourierTransform, however I got remaining $\Lambda$s in the terms of order $O(\mu^8)$ onwards. Thinking about this approach, I located the proble …
- 3,736
2
votes
Accepted
Can the derivative of eigenvectors with respect to its components be taken as zero if all ei...
I’ll try to explain it in physicists words:
A matrix with all eigenvalues equal is proportional to the identity matrix.
The eigenvectors are maximally degenerate, as every arbitrarily oriented orthono …
- 3,736