# Give a good explanation of determinants?

1. Feb 25, 2009

### nobahar

I don't think this goes under H/W questions, as it's not a specific question needing solving, or a proof, etc.
Getting back to the point, anyone know any good websites or sources that give a good explanation of determinants? I mean what they do, why they do it, not just how to do it. I googled and got pretty boring stuff that tended to be either simply how to do them or just...well... lacking excitment.
Thanks!

2. Feb 25, 2009

### yyat

Re: Determinants

Try to understand the formal properties (multilinearity) in terms of the interpretation as the volume of the parallelogram/parallelepiped (see the http://en.wikipedia.org/wiki/Determinant" [Broken]).
Determinants may not be the most exciting thing you will ever learn, but absolutely essential in almost all fields of math and applications of math.

Last edited by a moderator: May 4, 2017
3. Feb 25, 2009

### phreak

Re: Determinants

If you want to know why the determinant does what it does, pick up 'Analysis on Manifolds' by Munkres.

4. Feb 26, 2009

### nobahar

Re: Determinants

Cheers guys
I know what you mean by not the most exciting thing! Blimey, but I kind of get what you mean by important. I came across determinants reading about vectors.
Thanks again.

5. Feb 26, 2009

### Ben Niehoff

Re: Determinants

The determinant of an NxN matrix is equal to the oriented volume of the N-parallelepiped defined by the N column vectors (or alternatively, the N row vectors) of that matrix.

So for example, if you have a parallelogram defined by two vectors in the plane, (1,2) and (-1,3), then the area of this parallelogram is given by

$$A = \left| \begin{array}{rr}1 & -1 \\ 2 & 3 \end{array} \right| = (1)(3) - (-1)(2) = 5$$

which you can check geometrically, if you like.