Questions tagged [jordan-normal-form]

The Jordan normal form of a matrix is a similar block matrix having diagonal blocks when the matrix is diagonalizable and diagonal + nilpotent blocks more generally.

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Jordan form of the “multiplicative table” matrix

I have to find the Jordan form of the $(10\times10)-$matrix $A$ with the $n$th row formed by $n(1,2,3,4,5,6,7,8,9,10), \ \ 1 \leq n \leq 10$ I have calculated the determinant of $(A-xI)$ using ...
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find the Jordan form and $P$ such that $P^{-1}AP = J$.

Consider the matrix $$A = \left(\begin{array}{cccc} -11&0&-9\\32&1&24\\16&0&13 \end{array}\right)$$ I want to find the Jordan form of $A$, with $1$-s at the bottom and the ...
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Jordan matrix (de)composition

So any square matrix $A$ can be decomposed into $A = S J S^{-1}$ where $J$ has a normal Jordan form, moreover $A$ and $J$ are similar matrices. My question is quite straightforward. Given arbitrary ...
A non-nilpotent matrix $A\in \mathbb C^{2 \times2}$ has a square root
Is there any quick argument to show that every non-nilpotent matrix $A\in \mathbb C^{2 \times2}$ has a square root? Just the existence without computing it. Knowing that $A\in \mathbb C^{2 \times2}$ ...