Timeline for Eigenvalues are not the same in the special case
Current License: CC BY-SA 3.0
7 events
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| Dec 8, 2015 at 16:42 | comment | added | march | More importantly (as far as your note of precaution), Mathematica by default assumes that symbols appearing in mathematical expressions are complex, which often leads to these kinds of problems (although clearly that's not the problem in this case). | |
| Dec 8, 2015 at 15:14 | history | edited | Marvin | CC BY-SA 3.0 |
added 307 characters in body
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| Dec 8, 2015 at 15:09 | comment | added | Marvin | Interesting! I did not imagine that and was sincerely intrigued when you pointed out. I shall edit the answer accordingly. | |
| Dec 8, 2015 at 15:05 | comment | added | Daniel Lichtblau |
I wasn't actually making that up. In[174]:= evals1 = FullSimplify[Eigenvalues[h, Cubics -> True] /. x -> 0]; evals2 = Eigenvalues[h /. x -> 0, Cubics -> True]; SeedRandom[1111]; Chop[N[{evals1, evals2} /. e1 -> RandomReal[]]] Chop[N[{evals1, evals2} /. e1 -> RandomReal[] - 3*I]] Out[177]= {{3.25784305164, -1.18004698185, 2.}, {2., -1.18004698185, 3.25784305164}} Out[178]= {{2.92269893956 - 0.841588865026 I, 2., -0.366433003266 - 2.15841113497 I}, {2., -0.366433003266 - 2.15841113497 I, 2.92269893956 - 0.841588865026 I}}
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| Dec 8, 2015 at 14:59 | comment | added | Marvin |
I don't think it depends on the substituted value. For the said problem the value 2 will always match with the third element of Case 1, no matter what value of e1 is substituted. However, it might not be so for some other problem. It will be helpful to understand if you could give an example or mathematical reasoning.
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| Dec 8, 2015 at 14:55 | comment | added | Daniel Lichtblau |
There is a bit more to it than this. In the second case the first eigenvalue is 2 (independent of e1). If one substitutes a value for e1 then one eigenvalue in the first case will also be 2. But which one will depend on the substituted value. The point is that the two ensembles of eigenvalues agree, as they should. But they need not match up individually.
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| Dec 8, 2015 at 14:29 | history | answered | Marvin | CC BY-SA 3.0 |