other side. In general, this force will not be orthogonal to the surface, but it will depend on the orientation of the surface in a linear manner. This is described by a tensor of type , in linear elasticity, or more precisely by a tensor field of type , since the stresses may vary from point to point. Other examples from physics Common applications include: Electromagnetic tensor (or Faraday tensor) in electromagnetism Finite deformation tensors for describing deformations and strain tensor for strain in continuum mechanics Permittivity and electric susceptibility are tensors in anisotropic media Four-tensors in general relativity (e.g. stress–energy tensor), used to represent momentum fluxes Spherical tensor operators are the eigenfunctions of the quantum angular momentum operator in spherical coordinates Diffusion tensors, the basis of diffusion tensor imaging, represent rates of diffusion in biological environments Quantum mechanics and quantum computing utilize tensor products for combination of quantum states Computer vision and optics The concept of a tensor of order two is often conflated with that of a matrix. Tensors of higher order do however capture ideas important in science and engineering, as has been shown successively in numerous areas as they develop. This happens, for instance, in the field of computer vision, with the trifocal tensor generalizing the fundamental matrix. The field of nonlinear optics studies the changes to material polarization density under extreme electric fields. The polarization waves generated are related to the generating electric fields through the nonlinear susceptibility tensor. If the polarization P is not linearly proportional to the electric field E, the medium is termed nonlinear. To a good approximation (for sufficiently weak fields, assuming no permanent dipole moments are present), P is given by a Taylor series in E whose coefficients are the nonlinear susceptibilities: Here is the linear susceptibility, gives the Pockels effect and second harmonic generation, and gives the Kerr effect. This expansion shows the way higher-order tensors arise naturally in the subject matter. Machine learning The properties of Tensors (machine learning), especially tensor decomposition, have enabled their used in machine learning to embed higher dimensional data in artificial neural networks. Generalizations Tensor products of vector spaces The vector spaces of a tensor product need not be the same, and sometimes the elements of such a more general tensor product are called "tensors". For example, an element of the tensor product space is a second-order "tensor" in this more general sense,