# Determinant We can think of the determinant as how much a transformation *stretches* or *squishes* space. In other words, how does it change the *area*/*volume* of space. The answer is that the are gets stretched by a factor of *the determinant*; that is what the determinant *is*. For example, look at how the linear transformation below stretches space (we started with area = 1 and now have area = 6. )   So, in this case there is a scale factor of 6, which is the determinant. Note that here we found a scale factor *specifically for the area*. In other contexts we may be looking at similar figures (say triangles) and want to know how their area changes if we know their side lengths we scaled by a factor of $x$. In that case, we know the area grows by a factor of $x^2$. When using the determinant we are calculating this area scale factor directly. --- References * [3B1B Determinant](https://www.youtube.com/watch?v=Ip3X9LOh2dk&t=124s) * [Jacobian Determinat](https://www.youtube.com/watch?v=p46QWyHQE6M&list=PLSQl0a2vh4HC5feHa6Rc5c0wbRTx56nF7&index=73)