eigenvector

Noun

Meaning

(linear algebra) given a linear transformation



A


{\displaystyle A}

, a vector



x


{\displaystyle x}

such that



A
x
=
λ
x


{\displaystyle Ax=\lambda x}

for some scalar



λ


{\displaystyle \lambda }

(linear algebra) specifically, given a matrix A, the eigenvector of the transformation "left-side multiplication by A"

Synonyms

Related terms

Examples

Assuming that the matrix W is a primitive matrix ( irreducible and aperiodic ), then after very many generations only the eigenvector with the largest eigenvalue will prevail, and it is this quasispecies that will eventually dominate. Source: Internet

Each eigenstate of an observable corresponds to an eigenvector of the operator, and the associated eigenvalue corresponds to the value of the observable in that eigenstate. Source: Internet

Moreover, the eigenvectors are not unique because any linear combination of eigenvectors for the same eigenvalue is also an eigenvector for that eigenvalue. Source: Internet

The components of this eigenvector give the relative abundance of each sequence at equilibrium. Source: Internet

The weights can be computed from the corresponding eigenvectors: If is a normalized eigenvector (i. Source: Internet

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