Interactive tensor visualization
One way to get an intuitive understanding for tensors is as a function that ‘operates on’ an input vector. In the interactive example below, a tensor (represented as a 3x3 matrix) transforms the normal vectors of a unit sphere (yellow arrows); this is achieved using matrix multiplication.
We start with the identity matrix which leaves all input vectors, well, identical. Then, use the individual input fields to explore the characteristics of the transformations.