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#### lorenzoberto

##### New member

- Nov 23, 2021

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can you find all possible Jordan forms of T and related characteristic polynomial ? I am totally lost and that is the first time i see this type of problem

- Thread starter lorenzoberto
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- Thread starter
- #1

- Nov 23, 2021

- 1

can you find all possible Jordan forms of T and related characteristic polynomial ? I am totally lost and that is the first time i see this type of problem

- Jan 30, 2018

- 913

Note that x^3+ 3x+ 2= (x+ 1)(x+ 2). So -1 and -2 are eigenvalues and the "Jordan form" will include the block \(\displaystyle \begin{bmatrix}-1 & 0 \\ 0 & -2\end{bmatrix}\).

The other factor, \(\displaystyle x^7+ 2\) has the single real zero, \(\displaystyle -\sqrt[7]{2}\) and 6 complex roots, three pairs of complex conjugates. The Jordan form matrix will have \(\displaystyle -\sqrt[7]{2}\) on the main diagonal. a pair of complex conjugates, say a+ bi and a- bi, will give a submatrix of the form \(\displaystyle \begin{bmatrix}a & b \\ -b & a \end{bmatrix}\)