# 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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### Jordan normal form of sum of two commuting nilpotent matrices over a finite field (variant on a linear matrix pencil problem)

This question comes up with trying to construct Lie subalgebras of (large) Lie algebras that are invariant under a finite group $H$. I have two isomorphic $H$-invariant nilpotent subalgebras and am ...
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### How do I transform the matrix with similarity transformation to diagonal form and use this result to calculate $A^{10}$?

I have matrix $A=\left (\begin{matrix} -2 & -8 & -12\\ 1 & 4 & 4\\ 0& 0 &1 \end{matrix} \right )$ and I need to transform with similarity transformation to diagonal form. ...
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### Showing companion matrix is similar to Jordan block using Jordan-Chevalley decomposition

The Jordan-Chevalley decomposition says that given a linear operator $L$, you can decompose it as $L = S + N$, where $S$ is diagonalizable and $N$ is nilpotent. My textbook (Linear Algebra by ...
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I have a $5\times 5$ matrix and I need to find the Jordan form and its inverse. I know how to find the inverse. But for the Jordan form I am screwed. The matrix is $$\begin{bmatrix}3 & 0 & 0 ... 1answer 732 views ### Jordan blocks and the characteristic polynomial For A \in \mathbb{C}^{n,n} and \{ \lambda_1, \dots , \lambda_r\} are the eigenvalues of A. Then my lecture notes say that the characteristic polynomial of A is$$(-1)^n\prod_{i=1}^r(x-\...
I don't understand why it's apparently 'clear' that the matrix of $T$ with respect to the basis $v_1, \dots, v_n$ is a Jordan block of degree $n$ if and only if $v_1, \dots ,v_n$ is a Jordan chain for ...