## Link o' the Day

American Scientist has an interesting article about the future of computer storage (hint: video). Via /.

Wish me luck on my math midterm tomorrow.

In case you were wondering, this is the General Implicit Function Theorem:

Assume F maps R^{n+k} to R^{k} and is continuously differentiable. Also assume D_{y}F(x_{0}, y_{0}) is an invertible k by k matrix (where x is a point in R^{n} and y in R^{k}). Lastly, assume that F(x_{0}, y_{0}) = **0**. (**0** = {0_{1} ... 0_{k}})

Then, there exists r > 0 and the continuously differentiable function G(x) such that

1. F(x, G(x)) = **0** for all x such that ||x - x_{0}|| < r

2. If F(x, y) = **0**, then y = G(x) for all x, y such that ||x - x_{0}|| < r and ||y - y_{0}|| < r

3. D_{x}F(x, G(x)) + D_{y}F(x, G(x))DG(x) = 0 where DG(x) = D_{y}F(x, y)^{-1}D_{x}F(x, y)