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

Other articles related to "jordan block, jordan, block, blocks, jordan blocks":

Jordan Matrix
... In the mathematical discipline of matrix theory, a Jordan block over a ring (whose identities are the zero 0 and one 1) is a matrix composed of 0 elements everywhere ... The concept is named after Camille Jordan Every Jordan block is thus specified by its dimension n and its eigenvalue and is indicated as ... Any block diagonal matrix whose blocks are Jordan blocks is called a Jordan matrix using either the or the “” symbol, the block diagonal square matrix whose ...
Jordan Normal Form - Complex Matrices
... In general, a square complex matrix A is similar to a block diagonal matrix where each block Ji is a square matrix of the form So there exists an invertible matrix P such that P-1AP = J is such that ... J is called the Jordan normal form of A ... Each Ji is called a Jordan block of A ...

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