How to execute code on graphics processor?

Newbie question

I have a nVidia GeForce 6800 Ultra running with a dual Zeon 3.0 GHz and Linux
Knoppix v3.4. I am curious to see if it would be possible to offload the CPU by
moving some math operations in my program to the graphics processor on the video
card.

For example, assume that I have two matrices, A and B and I want to multiply
them together and store the result in a third matrix, C. Where
for (row=0; rowmaxRows; ++row) {
for (column=0; columnmaxColumns; ++column) {
C[row][column] = A[row][column] * B[row][column]
}
}
Instead of executing this code on the CPU, I want the main program to send this
to the graphics processor for calculation and then return the result back to the
main program.

I have a lot of experience with C/C++ programming, but none in interacting with
a video card. Are there any libraries, published API's, etc available to help
with this endeavor? Tips, comments, links, book recommendations, etc are
greatly welcomed.

Thanks.