# 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 $3×3$ matrices.
c) List all possible Jordan forms for $4×4$ matrices.
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Benedict
Step 1
Possible jordan forms of $3×3$ matrices are:
$\left[\begin{array}{ccc}\ast & 1& 0\\ 0& \ast & 1\\ 0& 0& \ast \end{array}\right],\left[\begin{array}{ccc}\ast & 0& 0\\ 0& \ast & 0\\ 0& 0& \ast \end{array}\right],\left[\begin{array}{ccc}\ast & 1& 0\\ 0& \ast & 0\\ 0& 0& \ast \end{array}\right]$
Step 2
Possible jordan forms of $4×4$ matrices are:
$\left[\begin{array}{cccc}\ast & 0& 0& 0\\ 0& \ast & 0& 0\\ 0& 0& \ast & 0\\ 0& 0& 0& \ast \end{array}\right],\left[\begin{array}{cccc}\ast & 1& 0& 0\\ 0& \ast & 0& 0\\ 0& 0& \ast & 0\\ 0& 0& 0& \ast \end{array}\right],\left[\begin{array}{cccc}\ast & 1& 0& 0\\ 0& \ast & 1& 0\\ 0& 0& \ast & 0\\ 0& 0& 0& \ast \end{array}\right],\left[\begin{array}{cccc}\ast & 1& 0& 0\\ 0& \ast & 1& 0\\ 0& 0& \ast & 1\\ 0& 0& 0& \ast \end{array}\right]$
Jeffrey Jordon