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Eigenvalue

Simple eigenvalue

Eigenvalue sensitivity

If $A(t)=A+tE$ and $\lambda(t)$ is a <differentiable function> defining a simple eigenvalue, then
$$
\lambda'(0)=\frac{u^TEv}{u^Tv}.
$$
The <Cauchy-Schwarz inequality> and the <operator norm> give
$$
|\lambda'(0)|\leq\|E\|_2s(\lambda).
$$

First-order perturbation of a simple eigenvalue

Past exam of the mathematics course of the University of Cambridge / 2017 / iii / Paper 336 / 1 / a / Solution

Past exam of the mathematics course of the University of Cambridge / 2023 / ii / Paper 4 / 40C / b / Solution

Past exam of the mathematics course of the University of Cambridge / 2023 / ii / Paper 4 / 40C / e / Solution

Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 345 / 1 / b / ii / Solution

First-order perturbation of a simple eigenvalue

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First-order perturbation of a simple eigenvalue

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