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,

Read more about this topic:  Defective Matrix

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