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Jordan Basis


A Jordan basis for a square matrix A is a vector basis consisting of chains b_(i,1),...,b_(i,k_i) satisfying

 Ab_(i,1)=lambda_ib_(i,1)

and

 Ab_(i,j)=lambda_ib_(i,j)+b_(i,j-1)

for 2<=j<=k_i. Such a basis provides the means by which any square complex matrix A can be written in Jordan canonical form.


See also

Jordan Block, Jordan Canonical Form

Portions of this entry contributed by Todd Rowland

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Cite this as:

Weisstein, Eric W., with contributions by Todd Rowland. "Jordan Basis." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/JordanBasis.html

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