Tensors

A Tensor is aN-dimensional Matrix:

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

ATensor is a generalization ofVectors andMatrices to higher dimensions.

Scalar

Vector(s)

Matrix

Tensor

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 aN-dimensional space, is called theRank of the tensor.

The rank is denotedR.

AScalar is a single number.

It has 0 Axes
It has aRank of 0
It is a 0-dimensional Tensor

AVector is an array of numbers.

It has 1 Axis
It has aRank of 1
It is a 1-dimensional Tensor

AMatrix is a 2-dimensional array.

It has 2 Axis
It has aRank 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 theScalar:

const scalar = 1;

Another simple math object is theArray:

const array = [ 1, 2, 3 ];

Matrices are2-dimensional Arrays:

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

Vectors can be written asMatrices with only one column:

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

Vectors can also be written asArrays:

const vector = [ 1, 2, 3 ];

Tensors areN-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 JavaScript library will save you a lot of headache.

One of the most common libraries to use for tensor operations is calledtensorflow.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 ...

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