# How can i do the divergence of a matrix 3x3?

1. Apr 18, 2007

### germana2006

How can i do the divergence of a matrix 3x3?

2. Apr 18, 2007

### HallsofIvy

Staff Emeritus
First explain what you are doing! "Divergence" is a vector valued differentiation of a scalar function. It is not, in general, defined on matrices. You could, of course, define it as what you get by applying the divergence to each component of the matrix. The result would be a matrix having vectors as components. How that would be interpreted depends on your original matrix- as a linear operator over a vector space.

And, of course, you haven't said anything about dependence on x, y, z or even how many variables there are. If the matrix were a constant, its diveregence would be "0" although I'm not entirely sure what kind of object that 0 would be!

Could you give more detail about the situation in which you are dealing with the "divergence of a matrix"?

3. Apr 18, 2007

### waht

Divergence is a scalar. Only a 1x1 matrix can hold a scalar.

4. Apr 18, 2007

### mathwonk

maybe he means divergence of a vector field on R^3 which could be viewed as a 3x3 matrix. does that make sense? (i am a little over the line at the moment.)

5. Apr 18, 2007

### robphy

Could he mean a "divergence of a tensor field" [which would be another tensor field of lower valence]?

6. Apr 19, 2007

### germana2006

Sorry, it's exact the divergence of a Tensor (3x3). I have to do the divergence of the anisotropic Diffusion coefficient in 3D, that's mean a Tensor of 3x3 components.
I think it is: the derivative of each component with respect x, y, and z. But i don't sure.