Unusual usages of linear algebra

[Mihulik]

Hello,
I'm preparing a presentation of linear algebra. Among other things, I'd like to present possible usages of linear algebra.
Besides the usual usages, I'd like to mention some very unusual ones.

I've tried googling but I didn't find anything interesting.


Please, do you know some unusual usages of linear algebra?
The more unusual or surprising, the better.:)

Thanks!

 

[epenguin]

If you can find anything interesting about linear algebra, that would be very interesting.

 

[Mihulik]

:-D Let's suppose interesting = not widely known:)

 

[Bacle]

How about applications to signal-processing using the Discrete Fourier Transform (maybe this is cheating a bit, in that we actually use inner-product spaces and
the concept of orthogonality)?

 

[Mihulik]

Yeah, that's a good example but it's not such an unusual example I'd like to find.:)
Something like, "I use linear algebra to whiten my teeth and pour my drinks," would be unusual enough.:)

 

[WWGD]

"I use linear algebra to whiten my teeth and pour my drinks," would be unusual enough.:)

You too? I thought I was the only one who did this?

 

[Mihulik]

So did I... So it's not as unusual as I thought it was:-D

 

[AlephZero]

Try googling for unusual uses of eigenvalues and vectors.

Two that I have come across over the years, in presentations at conferences, were in written language processing (trying to decide if two texts were written by the same author, etc) and forecasting results of sports contests from league tables of results.

Sorry, but I don't have any references to either of those - and I'm not going to start looking and do your research for you!

 

[Mihulik]

Thanks - that sounds good.:)

I'll do my "research" by myself, of course.:)

 

[chiro]

Hello,
I'm preparing a presentation of linear algebra. Among other things, I'd like to present possible usages of linear algebra.
Besides the usual usages, I'd like to mention some very unusual ones.

I've tried googling but I didn't find anything interesting.


Please, do you know some unusual usages of linear algebra?
The more unusual or surprising, the better.:)

Thanks!

Hey Mihulik and welcome to the forums.

One interesting application was using the spectral decomposition (eigenvalues and eigenvectors), to help find the Debauchies Wavelet scaling function and wavelet function.

For specifics take a look at:

http://rip94550.wordpress.com/2009/05/07/the-dyadic-expansion-of-daubechies-d4-scaling-function

and scroll down to finding initial values: This uses the spectral theory to get initial values so that we can find the scaling and wavelet functions for the Daubechies wavelet.

 

[Deveno]

linear algebra has some interesting applications to game theory, and weather forecasting, just off the top of my head.

 

[Pyrrhus]

Linear algebra is the language of econometrics. We (economist) refuse to use the index notation of physicists to do our matrix differentiation, and other methods. We heavily use linear algebra in our probability model formulations in econometrics.

You can take a look at Mathematics for Econometrics by Phoebus Dhrymes, or Matrix Algebra for Applied Economics.

 

[Deveno]

economics...weather forecasting...what's the difference?

 

[Studiot]

One aspect you might cover is the relationship between linear algebra and other parts of mathematics, such as graph theory or network theory. To find some unusual applications here you could look at the use of flowgraphs to solve electrical and structural networks.

The proof of virtual work as applied to a complicated truss is also a lesser known application of LA.

go well

 

[robphy]

http://www.rose-hulman.edu/~bryan/google.html

https://www.physicsforums.com/showthread.php?t=162737

 

[atyy]

I've tried googling but I didn't find anything interesting.

Google uses eigenvectors.

 

[Mark44]

If you can find anything interesting about linear algebra, that would be very interesting.

Personally, I think linear algebra is very interesting. Once you get beyond the mechanics of matrix operations and determinants and such, there are all sorts of interesting applications, such as solving systems of differential equations by diagonalization.

One of the more interesting applications related to linear algebra that I've seen is an error correction technique for CDs that one company (I believe it was Sony) developed. It's been a long while since I saw the presentation, so I'm light on the details. In essence, each digital audio sample on the CD (16 bits) had an extra block of bits, so each 16-bit word of data was part of a 20- or 24-bit vector of bits.

If I'm remembering the details, each of the vectors was a certain distance from all the others in the 20- or 24-dimension vector space, so if a certain block of data was computed to be closer to or farther from the others, the vector could be considered to contain one or more bad bits.

The fellow giving the presentation said that you could drill a 1/8" hole in the CD without losing any data. I've never tested this out, so it could be that this stuff wasn't actually put into production, but it struck me as very interesting. A Web search for CD or DVD error correction would probably turn up a lot more information.

 

[robphy]

www.science20.com/random_walk/ups_drivers_icosian_game_and_how_right_hand_turns_can_save_earth

en.wikipedia.org/wiki/Travelling_salesman_problem

http://en.wikipedia.org/wiki/Six_degrees_of_separation
possibly interesting links:
www.google.com/search?hl=&q=social+networking+matrix

(Linear Algebra is one of the tools used to study graph theory [as mentioned earlier in this thread])

google.com/search?hl=&q=computer+graphics+linear+algebra ...so... Photoshop, 3D-graphics, video games, robotics, Pixar movies, virtual reality, ...