a) List all possible Jordan forms for 3 times 3 matrices. c) List all possible Jordan forms for 4 times 4 matrices.

a) List all possible Jordan forms for 3 times 3 matrices. c) List all possible Jordan forms for 4 times 4 matrices.

Question
Matrices
asked 2021-03-07
a) List all possible Jordan forms for \(3 \times 3\) matrices.
c) List all possible Jordan forms for \(4 \times 4\) matrices.

Answers (1)

2021-03-08
Step 1
Possible jordan forms of \(3 \times 3\) matrices are:
\(\begin{bmatrix}* & 1 &0 \\ 0 & * &1 \\ 0&0&* \end{bmatrix} , \begin{bmatrix}* & 0 &0 \\ 0 & * &0 \\ 0&0&* \end{bmatrix}, \begin{bmatrix}* & 1 &0 \\ 0 & * &0 \\ 0&0&* \end{bmatrix}\)
Step 2
Possible jordan forms of \(4 \times 4\) matrices are:
\(\begin{bmatrix}* & 0 &0&0 \\ 0 & * &0&0 \\ 0&0&*&0 \\0&0&0&* \end{bmatrix} ,\begin{bmatrix}* & 1 &0&0 \\ 0 & * &0&0 \\ 0&0&*&0 \\0&0&0&* \end{bmatrix} , \begin{bmatrix}* & 1 &0&0 \\ 0 & * &1&0 \\ 0&0&*&0 \\0&0&0&* \end{bmatrix} ,\begin{bmatrix}* & 1 &0&0 \\ 0 & * &1&0 \\ 0&0&*&1 \\0&0&0&* \end{bmatrix}\)
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