# I wont to learn the logic behind a determinant

1. Sep 4, 2004

### paul-martin

I wont to learn the logic behind a determinant, the math isn’t so hard you do that then you do that, you don’t need to think.

But if I gone solve dynamic problems, then I must understand how a determinate work. Why do I get the information I want when I take the determinant?

Do anyone got an link which can help me in this?

Kindly paul-Martin....

2. Sep 4, 2004

### matt grime

I'm not sure that there is a "how" for the determinant's working. The determinant is defined to be the ratio of volume change of the unit n-cube. Do you mean why does it have the formula it does? Well, you could probably show that it were true geometrically, but that isn't very illuminating. If you know anything about exterior algebras, it can be derived from the fact that the n'th degree component of an n dimensional vector space's exterior algebra is 1 dimensional and the determinant is the induced image of the linear transformation on this component, but I don't know how useful that is to you. It is multiplicative and can be shown to be (essentially) unique and so on.

I don't see what this has to do with dynamics though.

Perhaps you could explain a little more what level you're at and what you mean by "how it works"

3. Sep 4, 2004

### HallsofIvy

What do YOU mean by "the information I want"?

4. Sep 5, 2004

### paul-martin

Well the problem i gott are something like this. (i have by accident wrote b instead of w)

http://img47.exs.cx/img47/4681/Determinant.jpg

Thx for any help given Paul-M.

5. Sep 5, 2004

### HallsofIvy

I will confess I was bemused for a moment by "angel speed"! (Calculating how fast an angel can fly? Is that before or after dancing on the head of a pin? ) I think you meant "angular speed" but anyway, you are seeking a value of w so that the matrix equation Ax= 0 has a non-trivial solution (A depending on w).

The "logic" of the situation is this: If A has an inverse, then we could solve the equation Ax= 0 for the unique solution x= A-10= 0. That is, if A has an inverse, then the equation has only the trivial solution. In order to have a non-trivial solution, A must not have an inverse.
A matrix has an inverse if and only if its determinant is not 0 and so does not have an inverse if and only if its determinant is 0. The equation Ax= 0 has a non-trivial solution if and only if det(A)= 0. You correctly set det(A)= 0 and correctly solved for w.