Question

What do you mean by generalized eigenvector?

Answer 1

Generalized eigenvector

• The generalized Eigenvectors of a matrix are vectors that are used along with the eigenvector of the matrix when the latter is not sufficient to form a basis because the matrix is defective.
• For a matrix $A$ of the order $m\times m$, with an Eigenvalue $\lambda ,$a $m\times 1$non-zero vector $x$is the generalized Eigenvector of $A$associated with the Eigenvalue $\lambda ,$if and only if there exists an integer $m>1$ such that ${\left(A-\lambda I\right)}^{m}x=0,$where $I$is the identity matrix of the order $m\times m$.

Hence, meaning of generalized eigenvector is explained.