Eigenvector
- Modern Physics -
Quantum Mechanics Dictionary
Definition
A mathematical structure used to represent quantum states and the operations performed on them. It specifies how states are expressed, related, combined, and decomposed into components that support calculation. It does not by itself determine physical predictions without a mapping to observables and measurement rules.
Eigenvector
Natural & Formal Sciences Dictionary
Definition
A nonzero vector in a vector space that an associated linear operator maps to a scalar multiple of itself, so that the operator acts by scaling (not rotating) on that one-dimensional direction.
Eigenvector
- Pure Mathematics -
Algebra Dictionary
Definition
A nonzero vector v such that Av = λv for some scalar λ (the corresponding eigenvalue); eigenvectors span eigenspaces and are defined up to nonzero scalar multiples.