guess the thread title says it all, what is a determinant?

guess the thread title says it all, what is a determinant?
They have quite a few uses but are usually matrices of coefficients for sets of linear equations.
They're used quite a bit in linear algebra.
Why don't you look it up?
yeah i looked it up. but the definitions can be pretty ambiguous.
How about a simple example?
Matrix (2 x 2)
{a b}
{c d}
The determinant of this matrix is a number ad  bc.
Determinant is a number defined for a square matrix. The rules for calculating this number are straightforward. See:
Determinant  Wikipedia, the free encyclopedia
Last edited by mathman; August 22nd, 2011 at 06:03 PM. Reason: layout fix
A determinant is an element that identifies or determines the nature of something or that fixes or conditions an outcome
No, I don't think this is quite right.
Suppose I let denote the set of all matrices with entries from the real field . Then the mapping is surjective but not injective.
Which in plain English simply means that for every there is a single real number but that this number is not unique, in the sense that any two or more different matrices may share the same determinant.
To claim that the determinant "determines" a matrix is to assert "show me the determinant and I'll show you matrix". For this to be true, the determinant mapping would have to be both surjective AND injective i.e. bijective i.e. have an inverse, and this is obviously not the case here.
« Is this the correct implementation of hessian normal form?  How to derive the rule of 70 from the basic mathematics of exponential growth? » 