Does anyone under stand a matrix of vectors?

[ken_rychlik]

My son is in college and has a course that deals with matrix. He tells me it is kind of like multiplying vectors, but I don't get it. I guess thats why I'm making sawdust and he's in school. Can anyone explain in plain english what a matrix is? This is mainly for him. I would like to understand it too if I could though.
Thanks
Kenneth

[bcammack]

I don't know if this will help or not. Math isn't my long suit (ironic as a computer professional, but... <shrug>).

http://en.wikipedia.org/wiki/Matrix_multiplication

[jseiler]

http://ocw.mit.edu/OcwWeb/Mathematics/18-06Spring-2005/VideoLectures/index.htm

[ken_rychlik]

Thanks and I will send those his way. It is over my head. His problems look like this one. (1.6i + 2k) x (.731i + 1.371j - 1.829k)

I understand the xyz thing but it throws in i,j, and k. Maybe it's getting away form 2d and towards 3d?

All I know is I'm lost and he needs a tutor. lol

Kenneth

[rcnewcomb]

In plain english:
Think of a load of buck shot fired out of a shotgun. Each piece is moving through space (xyz) and you can figure out each piece's position based on time since the shot was fired (t). That is one matrix.

Now imagine that buck shot passing though a heavy steel grate. Depending on the size of the slots in the grate, some buckshot will pass, others will not. It also depends on the angle of the grate relative to the buckshot and whether the grate is moving as well.

The math is tedious, but at least that gives you a mental picture (I hope).

[curtiss]

The last I heard on NOVA, "string theory" supports the need for 12 dimensions, not just 3 or 4 (the 4th being time...) I think there is a matrix in that mess somewhere.

Look for a 12 dimension Bot soon.

[jeffreymcgrew]

Randall's right. You can also think of it as if you're watching a creek. Things that float by, or things you drop into the creek, are going to take different paths depending on where they enter the creek due to the shape of the creek and the way the water is flowing through it. This sort of math helps you predict where the floating things will go if you know where the water is going first.

It's my understanding that this sort of thing isn't used just in solving physics problems, but is also used to solve certain problems that arise in Electronic circut design. So it's closer to your Shopbot than you might think!

[bcondon]

It has been way too long when I programmed Cad systems, if you take an object like a box, that has 8 corners on it... Each corner contains (X,Y,Z) in space. Now you rotate that box a little in the X direction, a little in the Y direction and a little in the Z direction, the combination of the (x,y,z) rotation affect the location of EACH corner of the box.

Multiplying matrices with the corner of the box (X,Y,Z) and the rotation of the box (XT, YT, ZT)
produces an exact location of each corner of the box in space (XFinal, YFinal, ZFinal) and you calculate that for each corner.

So where you see it in action is that many of the graphics cards in your computer perform those calculation in hardware. If you have a computer that does not have a graphics card in it with a graphics accelerator, then dynamically rotating an object in a CAD program must calculate EACH corner of the box... But with a good graphics accelerator, all of those calculations are done in the graphics card leaving your CPU to handle other tasks like capturing mouse events and clicks...

[dana_swift]

This is a risky thread to comment in.. but here goes!

A matrix is a tool for manipulating vectors. A shopbot is a tool for manipulating sawdust.

Simple enough?

There are other ways to manipulate sawdust other than a shopbot, and there are other ways to manipulate a vector other than a matrix.

Each one of them are one tool in their respective box of tools. A skilled craftsman learns all about the fine points of all the tools available and uses the appropriate one for the task.

Math has many tools, many of which are used by the shopbot. Therefore there is a relationship between matrices and sawdust I suppose. I will leave that for some graduate student..

D

[bcondon]

A good application of matrices to the Finish Carpenter is hanging cove molding. Then you get to an inside corner, if the molding laid flat against the wall(Like baseboard molding), you would cut both pieces (theoretically) at a 45 degree angle. Cove molding is tilted at the top at a 45 degree angle. The angle you now cut for cove molding inside corner is no longer 45 but something around 62 degrees because the Y direction tilt affects the base angle. If done completely through math, you would be applying a x and y transform matrix.

SO when high school students say "why do we have to learn all this stuff I will never use?" just give em an example with application and they will either learn it, or know who to call...