Such a matrix has each non-zero off-diagonal entry equal to 1, immediately
block. For example, in the above form J, we have the eigenvalues λ = 1 with.
1 . It is impossible to transform an arbitray matrix to diagonal form.
A Jordan canonical form consists of one or more Jordan blocks.
If you have an m×m Jordan block J with eigenvalue λ, then J−λI is nilpotent of order m; that is, (J−λI)m=0, (J−λI)m−1≠0. Note also that when ...
Consider a Jordan block of size k associated with an eigenvalue λ.
matrix of an operator corresponding to a specific Jordan chain written in reverse order. ((T − λI)k−1v,...,(T − λI)v, v) is a Jordan block. This is how we get a ...
In order to exchange two columns we multiply on the right by the same M.
be a complex matrix of order n where B has order n − 1. If J (A) has only one Jordan block, then. J(B) has only one Jordan block. Proof. The unique Jordan block ...
... whose Jordan form has a single non-trivial block were determined by