What are the independent terms in the Magnetic Tensor

[welshrich]

I am trying to understand the magnetic gradient tensor which has nine components. There are three magnetic field components, but there are also three baselines. These nine gradients are organised into a 3x3 matrix. I have read that only 5 of these terms are independent. What exactly does this mean? What makes them independent?

 

[dauto]

If five terms are independent than given those five terms you are able to calculate the others

 

[welshrich]

Thanks that is helpful. I had been trying to visualise what is happening and not having much success - I can imagine splitting the magnetic vector into 3 components and then measuring the rate of change of each of these particular components in the three directions. I did not realize you can use some of the terms in the matrix to calculate others. I assumed that only 5 remained because the others somehow canceled each other due to symmetry. And this is where I am hitting a wall - I can't imagine how the rate of change of one component of the field with respect to a given baseline can be equal to the rate of change of another component of the field with respect to a particular baseline. Any insights?