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Tensors

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.

ScalarVector(s)
1
1
2
3
 
1 2 3

MatrixTensor
1 2 3
4 5 6
 
1 2 3
4 5 6
 
4 5 6
1 2 3
 

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. R = 0.

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

A Vector is an array of numbers. R = 1.

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

A Matrix is a 2-dimensional array. R = 2.

  • 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).


Linear Algebra in JavaScript

In linear algebra, the most simple math object is the Scalar:

const scalar = 1;

Another simple math object is the Array:

const array = [ 1, 2, 3 ];

Matrices are 2-dimensional Arrays:

const matrix = [ [1,2],[3,4],[5,6] ];

Vectors can be written as Matrices with only one column:

const vector = [ [1],[2],[3] ];

Vectors can also be written as Arrays:

const vector = [ 1, 2, 3 ];

Tensors are N-dimensional Arrays:

const tensor = [ [1,2,3],[4,5,6],[7,8,9] ];

JavaScript Tensor Operations

Programming tensor operations in JavaScript, can easily become a spaghetti of loops.

Using a JavScript library will save you a lot of headache.

One of the most common libraries to use for tensor operations is called tensorflow.js.

Tensor Addition

const tensorA = tf.tensor([[1, 2], [3, 4], [5, 6]]);
const tensorB = tf.tensor([[1,-1], [2,-2], [3,-3]]);

// Tensor Addition
const tensorAdd = tensorA.add(tensorB);

// Result [ [2, 1], [5, 2], [8, 3] ]

Try it Yourself »

Tensor Subtraction

const tensorA = tf.tensor([[1, 2], [3, 4], [5, 6]]);
const tensorB = tf.tensor([[1,-1], [2,-2], [3,-3]]);

// Tensor Subtraction
const tensorSub = tensorA.sub(tensorB);

// Result [ [0, 3], [1, 6], [2, 9] ]

Try it Yourself »

Learn more about Tensorflow ...