In math, what is a tensor? How is it related to tensorflow from machine learning?
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Math at this level isn’t really for 5 year olds but in math, a tensor is an element of a special bilinear product ⊗ of vector spaces V and W such that for any biliear map *h* from the direct product of V and W to a different vector space Z, the special bilinear product commutes with a unique linear map *h’* to Z to create *h*.
So for vectors v in V and w in W, h bilinear: h(v,w)=h'(v⊗w) always has a linear solution h’ (a universal property). Here, v⊗w is called a *tensor*, and the space of all tensors here is denoted V⊗W. It requires the axiom of choice to assume the tensor product exists over infinite dimensional vector spaces. Tensor products over finite dimensional vector spaces give you n-dimensional arrays.
In machine learning, you’re messing with values in n-dimensional arrays to try to find an n-linear map X’ from the input space I to the outputs X(I) that approximates an unknown nonlinear map X. The process of updating a tensor with small changes over time to find X’ can be called a *flow*.
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