Eigenvector and matrix

[Macha]

Here's a little question that popped up this morning perhaps somebody knows the right answer:

Given a vector, is there a straightforward *cough* way in Houdini to find the matrix for which this vector would be the eigenvector?

[edward]

Sorry, I don't understand the question. How would you do so mathematically? If you know all the eigenvectors (and corresponding eigenvalues), then it's just two matrix multiplies. Anything else, it's an under-constrained problem and I'm not sure what you're trying to achieve.

[Macha]

Ah, Edward, I had a feeling I needed more information than just a single vector to solve this but wasn't sure. Thanks for the clarification.

I was thinking of alternative ways to scale random lines along their direction.

Just one of those random ideas that sometimes lead to something interesting. Maybe next time.

Edited August 12, 2011 by Macha

[Andz]

I was thinking of alternative ways to scale random lines along their direction.

Hey Macha, I haven't thought about it all the way to the end to see if it works but... have you tried:

1 - get 2 points from each line;

2 - subtract the two point (i have no idea what order you'll pick), to get the direction of that line;

3 - normalize that vector;

4 - multiply that vector by your scalar factor;

5 - redraw your lines using the first point on each plus this new vector.

[Macha]

Hi Andz. Yes, that's what I did, except that I used a displacement node rather than multiply. Same thing though. Would have been nice to have figured out a nifty matrix way for this.

[papicrunch]

Hi,

You can take a look at this post. Petz use some obscure mathematic (for me) related to eigenvector

have fun

Thomas

[edward]

The covariance matrix stuff is the same as computing an oriented bounding box ... eg. Bound SOP with Oriented Bounding Box enabled.