Difference between revisions of "What is Tensor?"
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In simplifying terms, we can think of tensors as multidimensional arrays of numbers, as a generalization of scalars, vectors, and matrices. | In simplifying terms, we can think of tensors as multidimensional arrays of numbers, as a generalization of scalars, vectors, and matrices. | ||
− | # Scalar, {{#tag:math|\mathbb{R} }} | + | # Rank 0 Tensor, Scalar, {{#tag:math|\mathbb{R} }} |
− | # Vector, {{#tag:math|\mathbb{R}^n }} | + | # Rank 1 Tensor, Vector, {{#tag:math|\mathbb{R}^n }} |
− | # Matrix, {{#tag:math|\mathbb{R}^n \times \mathbb{R}^m}} | + | # Rank 2 Tensor, Matrix, {{#tag:math|\mathbb{R}^n \times \mathbb{R}^m}} |
− | # 3 | + | # Rank 3 Tensor, Tensor, {{#tag:math|\mathbb{R}^n \times \mathbb{R}^m \times \mathbb{R}^p}} |
In simplifying terms, we can think of tensors as multidimensional arrays of numbers, as a generalization of scalars, vectors, and matrices.
When we describe tensors, we refer to its “dimensions” as the rank (or order) of a tensor, which is not to be confused with the dimensions of a matrix. For instance, an m × n matrix, where m is the number of rows and n is the number of columns, would be a special case of a rank-2 tensor. A visual explanation of tensors and their ranks is given is the figure below.
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