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What is an eigenvalue?

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Re: What is an eigenvalue?

#41

Post by cscheid »

ok123456 wrote: post #23
AdamH12113 wrote: post #2

Does anyone know of an example of a simple physical system where eigenvalues have a physical interpretation? The examples I know of are all in quantum mechanics, which is a bit abstract for me.

Markov probability matrix where the entries are probabilities of some physical event happening. The the eigenvectors will be the long term stable state probabilities.

The values associated with each vertex on the _dominant eigenvector_ (the eigenvector associated with the dominant eigenvalue) are the long-term stable state probabilities. That's from a single eigenvector, not "the eigenvectors".

Re: What is an eigenvalue?

#42

Post by Waterluvian »

Something that frustrates me, and maybe I’m just confessing my stupidity, is the extra layer of indirection in any discipline when things are named after people and not the thing’s characteristics.

My doctor once told me “if you learn enough Latin, a lot of names in medicine will hint at what they are, so you have less to memorize.”

I find that these names often lend a sense of complexity to concepts that turn out to be rather simple. In high school this really contributed to my struggles.

Edit: apparently Eigen isn’t a person’s name so I sure picked an embarrassing moment to bring this up.

Re: What is an eigenvalue?

#43

Post by _gmax0 »

hackandthink wrote: post #39

Machine Learning (LDA): "By finding eigenvectors we’ll find axes of new subspace where our life gets simpler: classes are more separated and data within classes has lower variance." https://medium.com/nerd-for-tech/linear-discriminant-analysi...

Also, if you come from a computing background, I think Eigenfaces is a great, illustrative use of eigenvalues.

https://en.wikipedia.org/wiki/Eigenface

Re: What is an eigenvalue?

#44

Post by ok123456 »

cscheid wrote: post #41
ok123456 wrote: post #23

Earlier quoted context omitted.

Markov probability matrix where the entries are probabilities of some physical event happening. The the eigenvectors will be the long term stable state probabilities.

The values associated with each vertex on the _dominant eigenvector_ (the eigenvector associated with the dominant eigenvalue) are the long-term stable state probabilities. That's from a single eigenvector, not "the eigenvectors".

Yeah each one is an eigenmode of the system. That's what I meant.

Re: What is an eigenvalue?

#46

Post by martin_balsam »

Waterluvian wrote: post #42

Something that frustrates me, and maybe I’m just confessing my stupidity, is the extra layer of indirection in any discipline when things are named after people and not the thing’s characteristics. My doctor once told me “if you learn enough Latin, a lot of names in medicine will hint at what they are, so you have less to memorize.” I find that these names often lend a sense of complexity to concepts that turn out to…

But it is named after its characteristic, albeit in German

Re: What is an eigenvalue?

#47

Post by sfpotter »

Waterluvian wrote: post #42

Something that frustrates me, and maybe I’m just confessing my stupidity, is the extra layer of indirection in any discipline when things are named after people and not the thing’s characteristics. My doctor once told me “if you learn enough Latin, a lot of names in medicine will hint at what they are, so you have less to memorize.” I find that these names often lend a sense of complexity to concepts that turn out to…

If you learn a lot of math, a lot of names will hint at what they are so you have less to memorize. :-)

Re: What is an eigenvalue?

#48

Post by Waterluvian »

martin_balsam wrote: post #46
Waterluvian wrote: post #42

Something that frustrates me, and maybe I’m just confessing my stupidity, is the extra layer of indirection in any discipline when things are named after people and not the thing’s characteristics. My doctor once told me “if you learn enough Latin, a lot of names in medicine will hint at what they are, so you have less to memorize.” I find that these names often lend a sense of complexity to concepts that turn out to…

But it is named after its characteristic, albeit in German

Well… boy did I pick the wrong example to bring this up with. Alas, I’ll leave my shame here for all to see.

Re: What is an eigenvalue?

#49

Post by idiotsecant »

AdamH12113 wrote: post #2

Does anyone know of an example of a simple physical system where eigenvalues have a physical interpretation? The examples I know of are all in quantum mechanics, which is a bit abstract for me.

Get a sheet of rubber. Grab it in both hands and stretch it. Inspect your sheet and find a line on the sheet that you could draw in with a marker and when you stretched the sheet the line would grow and shrink, but would not change what it was pointing at (probably a line from one of your hands to the other, in this simple example) That is an eigenvector of your sheet stretching transformation. The eigenvalue is how hard you're stretching the sheet.

Re: What is an eigenvalue?

#50

Post by Waterluvian »

sfpotter wrote: post #47
Waterluvian wrote: post #42

Something that frustrates me, and maybe I’m just confessing my stupidity, is the extra layer of indirection in any discipline when things are named after people and not the thing’s characteristics. My doctor once told me “if you learn enough Latin, a lot of names in medicine will hint at what they are, so you have less to memorize.” I find that these names often lend a sense of complexity to concepts that turn out to…

If you learn a lot of math, a lot of names will hint at what they are so you have less to memorize. :-)

Except when some smart jerk discovered like eight different things!
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