# 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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