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I want to calculate the JordanDecomposition of the follwoing matrix:

enter image description here

That is

mat= {
{ax^2 + ay^2, -ay bx + ax by, ax bx + ay by, -ax bx - ay by, -ay bx + ax by,  bx^2 + by^2}, 
{ay cx - ax cy, -bx cx + ax dx, by cx - ax dy, bx cy - ay dx, -by cy + ay dy, by dx - bx dy},
{ax cx + ay cy, -bx cy + ax dy, by cy + ax dx, -bx cx - ay dy, by cx - ay dx, bx dx + by dy},
{-ax cx - ay cy, -by cx + ay dx, -bx cx - ay dy, by cy + ax dx, bx cy - ax dy, -bx dx - by dy}, 
{ay cx - ax cy, -by cy + ay dy, -bx cy + ay dx, -by cx + ax dy, -bx cx + ax dx,by dx - bx dy},
{cx^2 + cy^2, -cy dx + cx dy, cx dx + cy dy, -cx dx - cy dy, -cy dx + cx dy, dx^2 + dy^2}
}

Remark: I wanted to use mathJax for the matrix, but unfortunately, I cannot do so because its considered bad formatted code.

Now if I try JordanDecomposition[mat], then I get the follwing error: General::eivn.

The help says that this occurs, if some of the expressions during the calculation simplify to zero but mathematica is unable to recognize this.

So, how can I avoid this?

A quick search showed me, that the JordanDecomposition function is not as useful as i thought. It does not consider all situations which can arise, only the general ones.
But I already know that for $b_x=b_y=c_x=c_y=0$ the matrix is diagonaliziable, and I am now interested in for which values this isn't the case anymore. So is there a better approach to this?

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  • $\begingroup$ @moo What do you mean? I simply copied my mathematica code $\endgroup$ – klirk Dec 16 '18 at 13:44
  • $\begingroup$ @Moo But i copied the mathematica code! $\endgroup$ – klirk Dec 16 '18 at 13:53
  • $\begingroup$ @Moo: are yout trolling me? The mathematica code is already there, but let me highlight it a little more: $\endgroup$ – klirk Dec 16 '18 at 14:08
  • $\begingroup$ @Moo Better now? $\endgroup$ – klirk Dec 16 '18 at 14:13
  • $\begingroup$ There may be structure to the formulas in mat that are not apparent, but the general symbolic Jordan decomposition of an arbitrary matrix can take many forms. Do you really expect to get them all, together with the conditions for each in terms of the 8 variables? $\endgroup$ – Michael E2 Dec 16 '18 at 23:53

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