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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

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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).