# Questions tagged [jordan-normal-form]

This tag is for questions relating to the Jordan normal form, also known as a Jordan canonical form or JCF of a matrix which is a similar block matrix having diagonal blocks when the matrix is diagonalizable and diagonal + nilpotent blocks more generally.

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### Is it true that for jordan block with zero eigenvalue we can choose basis where all diagonal elements are non zero?

Is it true that for jordan block with zero eigenvalue we can choose basis where all diagonal elements are non zero? if there is a proper number 0, then you can try to find a matrix in the form of J^(-...
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### Relation between Jordan Normal Form and cyclic modules

I've just started reading about the relation between cyclic modules and Jordan Normal Form and, being honest, I've quite a doubt. The text I am using says that "clearly", the following assumption is ...
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There a several ways to finding a jordan basis of a matrix $A$. For this question I have in mind two methods. Let $N=A-I\lambda$. Say we have already discovered several strings, say these two $v_1,... 1answer 50 views ### Generator for a Jordan basis associated with a Jordan block Let$M$be an$n\times n$matrix whose characteristic polynomial splits into$n$linear factors, so that there exists a Jordan canonical form$\mathcal{J}_M$of$M$. Now suppose$\lambda$is an ... 1answer 52 views ### Subspaces of generalised eigenspace If$A$is an endomorphism of a vector space$V$and$\lambda$an eigenvalue then$Ker (A-\lambda I) $is the eigenspace corresponding to$\lambda$and$V_\lambda=Ker (A-\lambda I)^{dim \ V} $is the ... 1answer 63 views ### Find all possible Jordan canonical forms of$4\times 4$complex matrices which satisfy the following three conditions simultaneously? Find all possible Jordan canonical forms of$4\times 4$complex matrices which satisfy the following three conditions simultaneously：$A$is not diagonalizable;$A$has characteristic polynomial$(x-...
A = $\begin{bmatrix} 1 & -1 & 0 & -1\\ 0 & 2 & 0 & 1\\ -2 & 1 & -1 & 1\\ 2 & -1 & 2 & 0\\ \end{bmatrix}$ I've been given this matrix - I'm supposed ...
How does the size of Jordan blocks in the Jordan canonical form of matrix A relate to exponents $d_i$ in the factorization of the minimal polynomial \$m_A(x) = (x-\lambda_1)^{d_1}(x-\lambda_2)^{d_2}\...