ktheory.com

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_yF(x₀, y₀) is an invertible k by k matrix (where x is a point in Rⁿ and y in R^k). Lastly, assume that F(x₀, y₀) = 0. (0 = {0₁ … 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 - x₀|| < r

2. If F(x, y) = 0, then y = G(x) for all x, y such that ||x - x₀|| < r and ||y - y₀|| < r

3. D_xF(x, G(x)) + D_yF(x, G(x))DG(x) = 0 where DG(x) = D_yF(x, y)^-1D_xF(x, y)

This entry was posted by site admin on Thursday, April 18th, 2002 at 9:10 pm and is filed under Tidbit. You can follow any responses to this entry through the RSS feed. You can skip to the end and leave a response. Pinging is currently not allowed.