Generalized eigenvector

In linear algebra, a generalized eigenvector of an n × n matrix ${\displaystyle A}$ is a vector which satisfies certain criteria which are more relaxed than those for an (ordinary) eigenvector.

Let ${\displaystyle V}$ be an n-dimensional vector space; let ${\displaystyle \phi }$ be a linear map in L(V), the set of all linear maps from ${\displaystyle V}$ into itself; and let ${\displaystyle A}$ be the matrix representation of ${\displaystyle \phi }$ with respect to some ordered basis.

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