Tensors

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In the last parts of our program we make use of the state of the art deep learning framework developed

by Google called tensor flow tensor flow works in a peculiar way.

But one of its main characteristics is that it works with tensors.

So it is only right that we introduce tensors now the mathematical concept of a tensor could be broadly

explained in this way.

A scalar has the lowest dimensionality and is always one by one.

It can be thought of as a vector of length one or a one by one matrix.

It is followed by a vector where each element of that vector is a scalar.

The dimensions of a vector are nothing but and by one or one by them matrices.

OK then we have matrices which are nothing more than a collection of vectors the dimensions of a matrix

are m by N.

In other words a matrix is a collection of and vectors of dimensions and by one or M vectors of dimensions

and by one.

Furthermore since scalars make up vectors you can also think of a matrix as a collection of scalars

to.

We know all that already.

Let’s get to tensors.

Now a tensor is the most general concept scalars vectors and matrices are all tensors of ranks 0 1 and

2 respectively.

Tensors are simply a generalization of the concepts we have seen so far and object we haven’t seen is

a tensor of rank 3 dimensions.

Are k by m by n it can be thought of as a collection of matrices in terms of programming tensor is no

different than in any array.

And in fact tensors can be stored in any arrays and that’s how we often deal with the issue.

Let’s create a tensor out of two matrices our first Matrix and one will be from the first example.

The Matrix M2 will be a different one with the elements 9 8 7 and 1 3 minus 5.

Now let’s create an array t with two elements and one and two.

After printing t we realize that it contains both matrices.

It is a two by two by three object it contains two matrices two by three.

Each all right if we want to manually create the tensor we would need to write this line of code.

As you can imagine tensors with lots of elements are very hard to manually create.

Not only because there are many elements but also because of those confusing brackets.

Usually we would load transform and preprocess the data to get tensors.

However it is always good to have the theoretical background.

This will do for now.

Thanks for watching.

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