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Jordan Block


A matrix, also called a canonical box matrix, having zeros everywhere except along the diagonal and superdiagonal, with each element of the diagonal consisting of a single number lambda, and each element of the superdiagonal consisting of a 1. For example,

 [lambda 1 0 ... 0 0; 0 lambda 1 ... 0 0; 0 0 lambda ... 0 0; 0 0 0 ... 1 0; | ... ... ... ... 1; 0 0 0 ... 0 lambda]

(Ayres 1962, p. 206).

Note that the degenerate case of a 1×1 matrix is considered a Jordan block even though it lacks a superdiagonal to be filled with 1s (Strang 1988, p. 454).

A Jordan canonical form consists of one or more Jordan blocks.

The convention that 1s be along the subdiagonal instead of the superdiagonal is sometimes adopted instead (Faddeeva 1958, p. 50).


See also

Diagonal Matrix, Jordan Canonical Form, Subdiagonal

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References

Ayres, F. Jr. Schaum's Outline of Theory and Problems of Matrices. New York: Schaum, p. 206, 1962.Faddeeva, V. N. Computational Methods of Linear Algebra. New York: Dover, p. 50, 1958.Golub, G. H. and Van Loan, C. F. Matrix Computations, 3rd ed. Baltimore, MD: Johns Hopkins University Press, p. 317, 1996.Strang, G. Linear Algebra and its Applications, 3rd ed. Philadelphia, PA: Saunders, 1988.

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Jordan Block

Cite this as:

Weisstein, Eric W. "Jordan Block." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/JordanBlock.html

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