With the recent addition of Numbers and some improvements of the documentation, Tensor now has reached version 1.0.0!

For people that do not yet know about it:

Tensor is a library that allows you to work with sparse Vectors, Matrices and higher-order Tensors, with the following nice features:

• An implementation of the Access protocol, so you can do mymatrix[42][3].
• It supports the arithmetic functions you would expect from vectors, matrices and tensors. These are implemented using Numbers, which means that they work on any numeric type.
• What is even more, Tensor itself implements Numbers’ Numeric behaviour, which means that anything that does number arithmetic can now do (elementwise) vector/matrix/tensor arithmetic! It also means that you can nest matrices ad infinitum!
• A sparse implementation: Only elements deviating from the default element of a data structure are stored. This means that e.g. a nearly-empty 10000x10000 element matrix takes up only a neglegible amount of memory.
• While you can work with numbers, you can store anything inside: Using it as a representation of a game board (a matrix for chess, or a 3-dimensional tensor for a Rubik’s Cube), for instance, is something that is very possible.
• Functions to rotate, transpose, transform, combine, separate, map over and reduce vectors/matrices/tensors.

Here are some examples from the Readme:

Vectors

iex> vec = Vector.new([1,2,3,4,5])
#Vector-(5)[1, 2, 3, 4, 5]
iex> vec2 = Vector.new(~w{foo bar baz qux})
#Vector-(4)["foo", "bar", "baz", "qux"]
iex> vec2[2]
"baz"
iex> Vector.add(vec, 3)
#Vector-(5)[4, 5, 6, 7, 8]
iex> Vector.add(vec, vec)
#Vector-(5)[2, 4, 6, 8, 10]

Matrices

iex> mat = Matrix.new([[1,2,3],[4,5,6],[7,8,9]],3,3)
#Matrix-(3×3)
┌                          ┐
│       1,       2,       3│
│       4,       5,       6│
│       7,       8,       9│
└                          ┘
iex> Matrix.rotate_clockwise(mat)
#Matrix-(3×3)
┌                          ┐
│       7,       4,       1│
│       8,       5,       2│
│       9,       6,       3│
└                          ┘
iex> mat[0]
#Vector-(3)[1, 2, 3]
iex> mat[2][2]
9
iex> Matrix.diag([1,2,3])
#Matrix-(3×3)
┌                          ┐
│       1,       0,       0│
│       0,       2,       0│
│       0,       0,       3│
└                          ┘

iex> Matrix.add(mat, 2)
#Matrix-(3×3)
┌                          ┐
│       3,       4,       5│
│       6,       7,       8│
│       9,      10,      11│
└                          ┘
iex> Matrix.add(mat, mat)
#Matrix-(3×3)
┌                          ┐
│       2,       4,       6│
│       8,      10,      12│
│      14,      16,      18│
└                          ┘

Tensors

  iex> tensor = Tensor.new([[[1,2],[3,4],[5,6]],[[7,8],[9,10],[11,12]]], [3,3,2])
  #Tensor(3×3×2)
        1,       2
          3,       4
            5,       6
        7,       8
          9,      10
            11,      12
        0,       0
          0,       0
            0,       0
  iex> tensor[1]
  #Matrix-(3×2)
  ┌                 ┐
  │       7,       8│
  │       9,      10│
  │      11,      12│
  └                 ┘

You can find it on Hex.pm and on GitHub.

And here in the Elixir Forum.