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This is discussion archived from a time before the current discussion method was installed.

[[Alex319]]: I presume this entry is named after the linear algebra concepts of "eigenvalues" and "eigenvectors". I know what those are but what do they have to do with this trope?

Firvulag: Orthogonality. The eigenvectors for a given linear system of equations are orthogonal to each other. You can't express one eigenvector for a system in terms of the other eigenvectors for that system.

For this sort of plot, it's one that forces every member of the team to solve a problem to achieve what ever it is they are supposed to be doing. That is you need each every member of the team because they are the only one who can solve their problem.

It runs into problems when the writer has to Hand Wave away reasons why two similar characters can't complete each other's tasks, or if the character's abilities and task don't really make sense in the overall problem.

Ie.

"Why didn't Superman pick up the big heavy thing?" "It had to be Wonder Woman, the big heavy thing... um can't be touched by men."

And

"Here comes Dracula and his sharks. Thankfully we have Aquaman with us."

<Phoenix> The name still fails to make sense to me. The driving concept behind Eigen Vectors isn't that they are orthoganal. For example, defining an Eigen Plot as one in which all the regualr elements of a plot are present, but scaled up, or down, would be more fitting (comparative to the usual of course) Perhaps "Perfectly Integrated Plot" would be more fitting. Or, if you want to keep vector terminology, go with "Hilbert Plot", they have all sorts of neat requirements (Norm from innerproduce, completeness, vector space, etc...) this would capture the "all useful properties needed angle."...

Zeke: The idea is fine, it's just not a good example. Think of it this way. You have your set of vectors (characters). Along comes a matrix (plotline) which just happens to be ideally suited to that set of vectors. Leaving out any character would fail to account for a dimension of the plot's effect, and when you apply the plotline to each character, the result fits that character perfectly. Or something.

The real problem with the orthogonality thing is just that it isn't true. Only a symmetric matrix is guaranteed to have orthogonal eigenvectors.

<Phoenix> Usually, one goes from operator to vectors, so your illustration appears to be in reverse. Given an operator A and an eigen vector e of A, we have Ae=ae, thus A(ke)=kAe=kae=ake. Hence, scalar multiples of eigenvectors are eigen vectors; thus this orthoganality thing is kinda senseless, they form a vector space; so do a million other things. Lastly, eigenplot is just as suitable as "Van Kampen Plot"; actually less: Van Kampen's Theorem involves connectivity and things lining up(intersecting) in the correct fashion.

Lull The Conqueror: Okay, I don't speak enough math to get in on the discussion of whether the name is good... but about the Harry Potter example: is this really an inversion? It seems like more of a justification to me. I mean, it's used pretty straight, but with a reason why things were designed this way. Then again, I haven't read the book this was in for a long time; is there some other element that makes it an inversion?
Janitor: Doesn't seem to have anyhting to do with the trope...
  • "Hello, and welcome to the Aperture Science Enrichment Center." The Center's purpose is to provide a safe testing environment to experiment on the Aperture Science Handheld Portal Device. With the Aperture Science Handheld Portal Device, the impossible becomes easy.

Pro-Mole: As far as I recall, there was no puzzle potions challenge on the movie. Apparently, they decided to show Hermione's abilities with the... plant. They still win the point for her "use of logic"...
Who the *** thought that the challenges in Un Lun Dun were all necessary to win the final battle? For one thing, each item must be sacrificed to get the next one. For another, the bishops didn't want to know who won. All she needed was the Un Gun. So Un Lun Dun is actually a parody of this trope.
Ophicius: Pruned Natter:
  • Carefully designed!? There's nothing carefully designed about The Doctors planning, they simply insert extreme technobabble which solves the problem when they feel like resolving the episode! They could just as easily have made up something about using extrapolator shielding of the Austerhagen device to blast them home or something.

Scialen: I'd just like to say that due to this trope I finally figured out why in my Astrophysics course we use the terms 'eigenvalues' and 'eigenfunctions'. If we assume that 'eigen' means 'specific' then it all makes sense to me now! Thank you TV Tropes! You have just helped me pass my Astrophysics masters!!

Pro-Mole: On the other hand, it took me some time to figure it out, since they were translated into Portuguese as "autovalues" and "autovectors". Just some trivia...
Pro-Mole: Could someone please make the Bokurano example more clear? I'm guessing those'd be Moji and Kirie, but a) I'm not sure how can anyone tell he was chosen against his will, and b) Kirie's fight didn't even happen in the manga, so there's no way to know. So, I might be totally wrong here.