Tensor

A generalized matrix(N-dimensional matrix), a finite table of numerical values indexed along several discrete dimensions.


Dimension of a tensor is the number of indices to specify one of its coefficients.

  • A 0D tensor is a scalar.
  • A 1D tensor is a Vector.
  • A 2D tensor is a Matrix.
  • A 3D tensor can be seen as a Vector of identically sized matrix.
  • A 4D tensor can be seen as a matrix of identically sized matrices, or a sequence of 3d tensors.
    Example:

Notes:

  • Rank, or Degree of a tensor: a Tensor’s Rank is the number of directions a tensor can have in a N-dimensional space(I.e. number of dimensions involved in a tensor).
  • A Scalar can be considered a 0-dimensional tensor(Rank of 0), vectors is a 1-dimensional tensor(Rank of 1), and matrices a 2-dimensional tensor(Rank of 2). however when talking about tensors, it’s assumed that it’s rank is higher than 2.