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So how do I plan to do this. Basically, I'm going to use color to visualize the action of the tensor as a linear operator. To do that, I need some user input, called the "input vector" v. The input vector v is multiplied by the tensor matrix M to produce an "output vector". We say that the input vector was "deflected" by M to produce the output vector. We use the output vector as the lookup into a spherical colormap such as this. Using one input vector, this process is performed everywhere in the dataset to assign a color to all the tensors. This process of multiplying a vector by the tensor matrix and looking at the result has physical meaning too. If the input vector is the gradient of the water density, then the output vector is the direction of water diffusion. If the material is isotropic, the input and output vectors are the same, but if the material is anisotropic, the matrix is going to be more interesting, and then the two vectors could be different.