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!

I don't really have any unusual uses off the top of my head, but I was always more impressed by how simple it makes so many of the usual problems rather than it being used in outlandish ways. Even though I know it's standard applications, and have known them for a couple years, I'm still amazed when I think, "How can I do X... *thinks* oh... it's just a matrix transform."

I don't know what level of audience this is aimed at (or what level you're at) - but the Fibonacci-sequence-by-matrix-exponentiation is a nice trick. Latent semantic indexing.

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

What kind of unusual are you talking about?

I mean, it is math for lines and spaces.

That is an incredibly huge topic, and just about anything you care to try is not unusual to those in that field.

You can map almost anything into it. Very few things can be realized mathematically but not represented (either directly or indirectly) using linear algebra.

There are the obvious uses for lines and geometric spaces. You can also use it for any type of decision surface and numerical problem spaces, such as a matrix representation of multiple equations or similar calculation grids. You can even use linear algebra when writing search engines, effectively treating each entry as a vector and finding the best matches.

You can encode any Turing-complete computing system into matrix form; meaning you can apply linear algebra to any kind of decision system that can exist. In other words, linear algebra can be used to encode any computing machine and any computable problem.


It's math. It does math things. I am not surprised by anything that I know it already does.

When I think of "unusual usage", I imagine things like "I use linear algebra to whiten my teeth and pour my drinks".

"I use linear algebra to whiten my teeth and pour my drinks".

That's exactly what I mean by "unusual usages".

Linear Algebra is generally used for solving systems of simultaneous equations. The first linear algebra book I read, had many examples in the field of thermodynamics. To some people, reasoning about lines and spaces with it is an unusual use.

A very quick Google produces:

• Determining Linear Dependence/Independence.
• Intelligent Information Retrieval (with Latent Semantic Indexing).
• Encrypting Text.
• Balancing Chemical Equations.

How about creating 3d video game engines?

I do remember using LA in graph theory stuff, and graph theory has applications to pretty much everything. Can't think of any specific examples, but graph theory touches so much you'll more than likely be able to find some cool stuff. edit: oh man! I totally forgot about adjacency matrices!

Pretty sure you could find applications for fluid dynamics also.

Stumbled on this, which is pretty much a paper on what frob said about search engines. http://www.rose-hulm...ersionFixed.pdf

Stumbled on this, which is pretty much a paper on what frob said about search engines. http://www.rose-hulm...ersionFixed.pdf

Didn't come from a web search for me; over a decade ago for a Master's level class on digital libraries we needed to implement and refine a vector space search engine for a series of assignments.

The class was just after Google's release, and most people in the course wrote up algorithms similar to what Google's early search functions were later revealed to be.

They have evolved a long way sense then, but a simple vector space model can do amazing things when it comes to searching text, which at first seems like very non-linear data.

To define unusual, it might help if youd mention what you consider to be usual first.

Anyway, many applications besides the textbook geometry have been listed already. Training neural networks is one I havnt seen mentioned yet.

Numerically solving field equations (fluids, electromagnetism, and so on) is another with a fairly high wow-factor, though hardly unusual.