!!! Overview [1] [{$pagename}] are geometric objects that describe linear relations between geometric [vectors], scalars, and other [{$pagename}]. Elementary [examples] of such relations include the dot product, the cross product, and linear maps. Geometric vectors, often used in physics and engineering applications, and scalars themselves are also [{$pagename}]. A more sophisticated example is the Cauchy stress tensor T, which takes a direction v as input and produces the stress T(v) on the surface normal to this vector for output, thus expressing a relationship between these two vectors, [{$pagename}] consists of a set of primitive values shaped into an array of any number of dimensions. A tensor's rank is its number of dimensions. Here are some examples of tensors: %%prettify {{{ 3 # a rank 0 tensor; this is a scalar with shape [] [1. ,2., 3.] # a rank 1 tensor; this is a vector with shape [3] [[1., 2., 3.], [4., 5., 6.]] # a rank 2 tensor; a matrix with shape [2, 3] [[[1., 2., 3.]], [[7., 8., 9.]]] # a rank 3 tensor with shape [2, 1, 3] }}} /%!! More Information There might be more information for this subject on one of the following: [{ReferringPagesPlugin before='*' after='\n' }] ---- * [#1] - [Tensor|Wikipedia:Tensor|target='_blank'] - based on information obtained 2017-08-08-