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The simple spectral projector
Definition
Let be a simple eigenvalue of , and let be compatible nonzero right and left eigenvectors. Since , the rank-one map
is well defined. It is the simple spectral projector onto the eigendirection along .
Depends on
Used by
- The reduced resolvent, or group inverse, on the complementary invariant subspace of a simple eigenvalue Definition
- The reduced resolvent satisfies the standard projector and inverse identities on the complementary invariant subspace Proposition
- The simple spectral projector is unchanged by nonzero rescalings of the left and right eigenvectors Proposition
- The derivative of the simple spectral projector is expressed by the reduced resolvent and the perturbation Theorem
Dependency tree · two levels
2 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.
Sources
- David Bindel, CS 6210: Matrix Computations - Perturbation theory (standard reference, not scraped)