A vector is an eigenvector of a linear map (transformation) if the map merely scales the vector up or down (makes it larger or smaller), but does not change its direction.

Really good intuitive link:

<link>

So think of it this way.

You have a certain opinion and when someone argues with you about it, it merely makes you hold the opinion more strongly. So in a very real sense, your opinion is an eigenvector of his argument.

Alternatively, you have the same opinion but when someone argues with you about it, it merely makes you hold the opinion less strongly (but does not make you say "I've changed my mind.)

Your opinion is also an eigenvector of that person's argument.

I once did an old-fashioned sociogram of the old Fray (which I believe Cat may still have somewhere.)

But it would be much more interesting to figure out which of each of our opinions are eigenvectors for which of whose arguments.

I just hate, almost, Da Vinci's Mona LIsa ... I absolutely hate the song too.

This painting by him <link> on the other hand, is simply breathtakingly exquisite.

I don’t know. When challenged on an argument I litmus test the case against the principles I subscribe to. I’ve had my mind changed here and also had my opinions bolstered here. I don’t (I think) automatically hold the opinion more strongly as a result of its challenge (though I could be wrong on that). But the fact that I’ve had positions altered by superior arguments that better adhere to the framework I work within would suggest otherwise.

I’ve no idea who my opinions are eigenvectors for—or vice versa. Is it still an eigenvector if the position and counterargument are tested against ontological standards? I’m not sure. I suspect it would depend upon whether both parties conceded the standard as a legitimate litmus test. That would be hard to achieve or verify.

Just thinking out loud. But it's a really good question regardless and warrants an uprate because of that.

I think maybe a litmus test for determining whether or not you are spending too much time here might be when you notice that such questions are striking you as reasonable.

On the other hand, your post might be seen as a counterpoint to August's, so there is that.

my trigger finger. That dark mark under her arm looks like a shot pattern to me. Here's something neat: at first I thought, if the angel really arrived airborne, her wings wouldn't be in that position. (S)he didn't land on one knee. (S)he landed on his/her feet and then dropped to one knee as a sign of reverence for Mary. But then I recalled that, when ducks hit the water, they often do lift their wings several times to shake off the drops that landed on them. So Leonardo's posturing of the angel as a just-landed duck is actually quite accurate.

You're right, it is an exquisite painting. Never cared for Leonardo. Too cold, precise. This painting is that, but it seems to burn with an inner life (that may not be accessible to me). The expression on the angel's face is irreplaceable. If I saw that look on somebody, I'd damn well salute and say, "Whatever you say." Leonardo manages to make Mary look equal to the situation.

First, he got the most basic premise of the eigenvector wrong (direction; see first paragraph of his link). The answer if we just think of the question and not his explanation, is everybody, everything.

We're all on the same line. We agree (Iraq war, abortion, stimulus, tempo's poetry, ciinc is full of shit, etc), we disagree. Strongly or weakly. Imagine a line (scale) from -10 (strongly disagree) to +10 (strongly agree). Our personal vector is from 0 to whatever for a particular argument. Put me at +9 for the fifth example. Now, what am I after I hear X's opinion (my person X eigenvector)? He's looking for eigenvalues. Greater than one strengthens my opinion, 0 to 1 weakens it, 0 to -1 weakly reverses it (relatively speaking, on the scale I'm now paying homage somewhere between 0 and -9), greater than negative one strongly reverses it.

Notice her left hand - giving the stop signal. What she's hearing is too much of a shock.

There's a long bad tradition of painting The Annunciation with a compliant Mary looking rather dumb. Here, though, is an Annunciation worth talking about. Mary is starting to shield herself - almost rejecting the news. That's nice. This Campin from 1420 is in this vein too.

First, he got the most basic premise of the eigenvector wrong

You're predictable, but in this case wrong.

I think the problem here is that in your need to claim me misconceived, you introduced an assumption of your own that is precisely the opposite of my starting premise.

Your assumption is that EVERY opinion that each one of us has about any topic can be influenced in some way by EVERY argument of anyone else's about the topic.

That's why you think I've confused eigenvectors and eigenvalues, when in fact I haven't.

What's of interest to me is the fact that in real life, as at BotF, many maps (arguments) don't "scale" any of our opinions at all.

So, our opinions are only eigenVECTORS for those arguments which scale them, and only when one of our opinions IS an eigenVECTOR of someone else's argument can we talk about the matter of eigenVALUES (degree or amount of scaling), and of course, scaling that includes reversal of vector orientation without changing vector "direction" (scalar multiplication by -k.)

Try changing your locks - it may help.

Who is the Fray-yin to my Fray-yang?

Perhaps better yet - who is the Fray anima to my animus ? (Sorry - couldn't resist that little pun-g.)

But yeah, either one does illustrate the idea that what's being discussed here is the way in which certain maps pick out certain eigenvectors.

For example, there is no opinion (vector) of mine which is an eigenOPINION of any of Skeppy's argument's (maps.) (Perhaps because Skeppy's arguments are always non-LINEAR, in which case they can't have eigenvectors at all - heh heh heh - sorry again - couldn't resist that one either.)

You don't know what a vector is. (Nor an eigenvalue of unity, but you can hardly be faulted for that.)

Is it still an eigenvector if the position and counterargument are tested against ontological standards?

Your question is interesting, Demo, because it goes to the point that all discussion of eigenvectors/values/maps assumes a specific choice of basis.

In the geometric case, this is usually the familiar "Euclidean" basis(1,0,0), (0,1,0), (0,0,1) for familiar 3-D space, but it doesn't have to be.

Similarly, one might say that when people aren't "communicating", it's because they're each stating their opinions (vectors) and arguments (maps) with respect to entirely different bases.

Did Pascal hear Jesus in the night, saying "On this basis shall I build my church?"

I would expect better than that from you.

Here's a column vector:

[1,1,1].

It's an eigenvector of the symmetric (diagonalizable) map M consisting of the 3x3 matrix whose rows are

0 1 5

1 4 1

5 1 0

(because 0*1 + 1*1 + 5*1 = 6 and 1*1 + 4*1 + 1+1 = 6 and 5*1 + 1*1 + 0*1 = 6.)

Or are you claiming otherwise?

As I said, if you'll simply change your locks, you'll see there's no harm in admitting that you missed my point (in a way that Demo and TK clearly didn't.)

You may have missed (or misstated) something fairly fundamental (akin to the infamous even/odd gaffe) to which daveto is reacting. Your top-post asserted the following:

A vector is an eigenvector of a linear map (transformation) if the map merely scales the vector up or down (makes it larger or smaller), but does not change its direction.

That assertion is only true of all eigenvectors of the transformation that have a positive eigenvalue. Eigenvalues can be negative. In that case, what happens to the eigenvector to which it corresponds?

(There's no harm in admitting that your premise may have been flawed and non-representative of your point)

Uhh -

Your objection (and daveto's) is based on the odd assumption that although I said "if", I must have meant "iff".

But of course, I meant precisely "if" and not "iff" because "if" suffices to specify the domain of discourse in which I wanted to make my observation.

Perhaps you should also think about changing your locks - i.e. consider why you (and daveto) CHOSE to assume I meant "iff"

Your gaze wanders yet the eigenvector up your butt is a constant reminder of your core being.