Defective Matrix - Jordan Block

Jordan Block

Any Jordan block of size 2×2 or larger is defective. For example, the n × n Jordan block,

$J = \begin{bmatrix} \lambda & 1 & \; & \; \\ \; & \lambda & \ddots & \; \\ \; & \; & \ddots & 1 \\ \; & \; & \; & \lambda \end{bmatrix},$

has an eigenvalue, λ, with multiplicity n, but only one distinct eigenvector,

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