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In this section, we shall start with tensor basics.

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Then we'll move on to casting and tensor flow.

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We'll look at initialization, indexing, broadcasting, algebraic operations, matrix operations,

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commonly used functions in machine learning.

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We'll look at the different types of tensors, like the ranked tensors, sparse tensors and even the

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string tensors in the context of deep learning.

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Tensors can be defined as multi-dimensional arrays.

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An array itself is an ordered arrangement of numbers.

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It's important we take note of these keywords as the data we shall be dealing with.

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Like, for example, this image right here can be represented using this numbers which have been arranged

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clearly in an ordered manner and can be represented in multiple dimensions.

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In this specific case, we have this array which is represented in one two dimensions.

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So this is A to Z or two dimensional array or what we generally call a matrix.

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Now we'll explore different types of arrays based on their dimensionality.

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So here, for example, we have what we'll call a zero dimensional array, which is simply because this

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array or this tensor contains a single element.

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So let's say we have 21.

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This is a zero dimensional array.

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Let's say we have one, this is zero dimensional, so on and so forth.

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So essentially once we have a single element, then it's A0D array.

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And then now for our next example, we have this 1D tensor right here, which in fact is a combination

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of several zero D tensors.

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So if you look at this, you see that this is A0D tensor, this is another zero D tensor, this is another

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zero D tensor.

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So this vector is made of three of these kinds of elements.

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Now, we could have other examples like this.

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Let's say we have five, um, eight and then three.

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Oh, let's, let's, let's change the length.

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So let's say we have one of length five, for example, we could have ten two, 11, four and seven.

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So this is a 1D tensor we have right here.

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So, so far we've looked at the zero D tensor, we've looked at the 1D tensor and now we could dive

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into the 2D tensor, which essentially is made of a combination of several 1D tensors.

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You could see that right here.

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This is a 1D tensor here, this is another 1D tensor, this is another 1D tensor.

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And finally here we have a 1D tensor.

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So when you bring together this 1D tensors, you form this 2D tensor for a three dimensional tensor.

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You might have guessed this right?

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You would simply combine several two dimensional tensors.

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So right here we have this 2D tensor with this other 2D, with this other 2D and this other 2D forming

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a 3D tensor.

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We could visualize this differently here.

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So we take this, this, this and this.

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Now you see we have one, two and the third dimension.

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Now that we understand this, we are going to take a look at the concept of tensor shapes, starting

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with this.

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Given that it's zero dimensional, then there is no shape with this one here.

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It's one dimensional and it's made of three elements.

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And so we could say this is of shape three.

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So we have three and that's it.

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Now for this other one, it's made of one, two, three and four 1D tensors, and each and every one

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of these is made of three elements.

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So this here, for example, is made of three elements.

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This made of three, this three, this three.

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And given that there are four of this made of three elements, its shape is four by three.

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So that's it.

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That's how we obtain the shape for this.

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Now for the 3D tensor we have here is made of one, two, three, four 2D tensors.

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So this year we have four two uh, 2d tensors and each and every one of these is made of two 1D tensors

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where each and every one is made of three elements.

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So what we'll see here is this is two by three this year because we have one, two is two by three,

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this is two by three and this here is two by three.

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And now given that we have four of this different two by three 2D tensors, then we would say the shape

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of this 3D tensor is four by two by three.

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So similar to this, we have four by three.

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This is four by two by three.

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Now notice that the number of elements we have here tells us or gives us information about the number

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of dimensions our tensor is.

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So here because we have a 1D tensor or one dimensional tensor, we have just one here because it's 2D

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or two dimensional, we have two and here because it's 3D, we have three.

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Also in matrix notation, we would say that this year or this matrix right here is made of one two.

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Three and four rows.

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So number of rows we have here is four.

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And then here we have one, two, three columns.

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Number of columns is three.

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In the case of this 3D tensor we have right here, we have one two rows and one, two, three columns

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for each and every one of this 2D tensor we have right here.