A Tensor is a N-dimensional Matrix:

  • A Scalar is a 0-dimensional tensor
  • A Vector is a 1-dimensional tensor
  • A Matrix is a 2-dimensional tensor

A Tensor is a generalization of Vectors and Matrices to higher dimensions.

Tensor Ranks

The number of directions a tensor can have in a N-dimensional space, is called the Rank of the tensor.

The rank is denoted R.

A Scalar is a single number.

  • It has 0 Axes
  • It has a Rank of 0
  • It is a 0-dimensional Tensor

A Vector is an array of numbers.

  • It has 1 Axis
  • It has a Rank of 1
  • It is a 1-dimensional Tensor

A Matrix is a 2-dimensional array.

  • It has 2 Axis
  • It has a Rank of 2
  • It is a 2-dimensional Tensor

Real Tensors

Technically, all of the above are tensors, but when we speak of tensors, we generally speak of matrices with a dimension larger than 2 (R > 2).