darkpsi
Apr30-11, 04:41 PM
Hello all,
I am reading a research paper and have found the equation below:
http://latex.codecogs.com/gif.latex?\mathbf{z}%20=%20\mathbf{a}%20-%20%28\nabla^2E%28\mathbf{t}%29%29^{-1}\Delta%20E%28\mathbf{t}%29%29
in which E is some function with the variable t being the vector input, and a and z being unimportant other vectors.
Now, it's my understanding that the Laplacian of a vector is the same as the divergence of the gradient, but in this equation they are being treated as separate operations, namely because division would result in 1 which would be meaningless. I'm not sure if the first part is taking an inverse, if the two operations are not the same, and/or something else entirely. I can provide more information if it turns out the equation or vectors make the difference.
Thanks for any help!
I am reading a research paper and have found the equation below:
http://latex.codecogs.com/gif.latex?\mathbf{z}%20=%20\mathbf{a}%20-%20%28\nabla^2E%28\mathbf{t}%29%29^{-1}\Delta%20E%28\mathbf{t}%29%29
in which E is some function with the variable t being the vector input, and a and z being unimportant other vectors.
Now, it's my understanding that the Laplacian of a vector is the same as the divergence of the gradient, but in this equation they are being treated as separate operations, namely because division would result in 1 which would be meaningless. I'm not sure if the first part is taking an inverse, if the two operations are not the same, and/or something else entirely. I can provide more information if it turns out the equation or vectors make the difference.
Thanks for any help!