# 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,

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

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... 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 ... J is called the Jordan normal form of A ... Each Ji is called a Jordan block of A ...
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... 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 ... 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 first diagonal block is, whose second diagonal block ...

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No contact with savage Indian tribes has ever daunted me more than the morning I spent with an old lady swathed in woolies who compared herself to a rotten herring encased in a block of ice.
Claude Lévi-Strauss (b. 1908)

As a child I was taught that to tell the truth was often painful. As an adult I have learned that not to tell the truth is more painful, and that the fear of telling the truth—whatever the truth may be—that fear is the most painful sensation of a moral life.
—June Jordan (b. 1936)