What is a Tensor Rank and Tensor Shape - TensorFlow

In this article, we will learn about Tensor Ranks and Tensor Shapes.

We know a tensor is an n-dimensional array. So, Rank is defined as the number of dimensions of that tensor. And, Tensor Shape represents the size of the each dimension.

Dimension levels

A tensor with rank 0 is a zero-dimensional array. The element of a zero-dimensional array is a point. This is represented as a Scalar in Math and has magnitude.

Eg: s = 48.3

Shape - []

A tensor with rank 1 is a one-dimensional array. The elements of the one-dimensional array are points on a line. This line has magnitude, direction. and is represented as Vector in Math. Vector has n entries.

Eg: v = [1, 9, -6, 7, 0]

Shape - [5]

A tensor with rank 2 is a two-dimensional array. The elements of the two-dimensional array are lines on a surface. This surface is represented as a Matrix in Math and has two coordinates. The Matrix contains n x n entries.

Eg: m = [[2.4, 5.1], [3.3, 7.9], [8.5, 6.1]]

Shape - [3, 2]

A tensor with rank 3 is a three-dimensional array. The elements of the three-dimensional array are surfaces of a cube. This is represented as a 3-Tensor in Math and has three coordinates. 3-Tensor has n x n x n entries.

Eg: t = [[[2, 5, 6], [5, 3, 3], [6, 7, 8]], [[0, 0, 1], [9, 7, 9], [2, 3, 6]], [[4, 8, 2], [1, 0, 8], [4, 4, 0]]]

Shape - [3, 3, 3]

You can continue increasing the entries to create a 4-Tensor, 5-Tensor, .... n-Tensor. n-Tensor has n x n x n x n .... n entries, while it's shape is [n, n, n, n, n, ... n]

Below is the code snippet that creates tensors with different ranks and shapes. Play with it.


  1. This explains better than tensorflow official tutorial, thanks


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