[BOŞ_SES] Hello. In our preceding session, linear processor We called transformation, transmission, we were saying, we have described. There was this issue: a t x processor is giving a year. This x a m n-dimensional space from dimensional space in essence a transport operation. It is important that we see the order of the transaction, In the non-linear processor. This is just where we met two alien to the already naturally. x where real space, we call them space definition. space where the x and y take on another space We are carrying, which we call the target space. Now let's bring them in a little more detail. We see immediately that: u and v transportation In space, plus there is also access to space. Not just because of the result of a linear processor. Because we see that gives us a tx, ty gives a van. Each of these objectives in the same space. Under Target it is closed for the collection, plus there is also space in this space. Yet there is an important vector. If any moving vector is zero, for example, if moving to zero x, y, also moving to zero if, It may have been more than moving the same zero vector; When we receive the x plus y, x plus y, t is linear processor For TX tyler will be plus. These u plus v, we say but each of which are zero vectors. Therefore, if you are moving to x is zero, y is the sum of them will be moved to zero when moving to zero. Similarly, x is moved to zero three times. Therefore, an important task to do zero. This reveals the two of us need more space. This cluster of y t We call transport space of the processor. English word is used in the range. This is different from the target space to reach the target space We are trying, but we may also turn off all of the target space. So the difference between these. Transportation space, we reach parts. That is a bad analogy, but maybe you're shooting somewhere, You shoot a huge wall, but instead, but can reach a certain Or, you do a shot into space, you göderiy a missile instead of a certain You can reach, you may also reach some places, therefore transport targeted different in this respect. We see that it is important for the zero space. If zero space is defined as follows: x If x reaches zero, we will see, zero always goes to zero in a linear processor. But if the X out of it, the space created for them we say zero space. Now, it looks like an abstract of these concepts before my görselleştirel. Then clarify the sample. There is this space: we call this definition of space, t is defined for each item in this space. And also defined as linear. Order here we are carrying the elements of a target space. But there can be a part of this target is reached space. We call this access to space. There are also inaccessible sections, so here's elements If we take, for example, take a missile again, you're into this space shooting but can not reach anywhere, you can only get to this part. Another important space in, here you can visit some elements always zero space. Annihilator in this t Always when we fetch target Located in the space to be found in the transport space. All, must have an element of up to zero, there are at least zero. So here is zero, zero vector as well. But the issue of whether the vectors outside of the zero vector. Now we will set the example for them. Soon the example, there are two definitions. The size of the space shuttle is one of them. This is called to order. The dimension of the zero space, You can also call it the dimension of the null space or spaces can say, Due to this gap: where the items are just going to zero, do not go somewhere else. In that respect in this space, We can think of it as creating a space within a space definition. English expressions are down something like, which also serves as an internationally recognized term. We find now that inequalities: it was the size of the space can be accessed order. This is a subspace of the target space, hence this order can not be larger than the size of the target space. Small or may be equal. If the gap is still there. It also space, that space is made up of zero to the zero vector, definition of a subspace space. Therefore, it can not be larger than the size of the space definition, The space can be up to a maximum definition. He has a theory: that to be undefined, we give the proof. The size of the space definition, ie with the order the size of the space shuttle is equal to the total size of the zero space. This is an extremely important theorem. Many also offer the ability to check account is also forecasting Using this feature gives the possibility of using this theorem. Some things are impossible to predict without the accounts. Just as an added here the following two inequalities We are removing a third inequality. But when you add the size of the order null space definition can access the size of the space. Therefore smaller than the size of the order definition space, as it is less than the size of the target space, for different reasons. Here transportation space, because it is a subspace of the target space Because a smaller space, which can be located as we can visually see because it is part of the target space, the size can not be larger. Similarly, the results of this theorem transport All descriptions of the size of the space indicates not be greater than the space dimension. The first results can be obtained in a more simple manner, The second basis of this theorem, d is due to the work of international show notation is used for the definition of the domain. There is also a one-processor concept. If you only have zero zero space, MARGIN we call it zero, but zero zero in the space If there are elements then it becomes a zero space with a certain size. He can go to zero, but many take the zero vector. Here we look at any number of space space, a hit with a number of the zero vector space Another vector, any vector eklesek, As you can see this because t is linear We sequence the transforms x before we make changes, n, and then we transform alfayl We stood, t that would be a plus zero conversion. Because the definition of n zero conversion. Thus we encounter as a result: If zero If only the zero vector space, There is nothing we can add then any transformation. This one to one conversion happens. That comes from a single x opposed opposed to each y. But if there are other vectors of the zero space zero vector, which When we get hit by any of the new vector with a number. Once the new vector x plus alpha, so more than y, As it can be obtained by changing the alpha, an infinite number of vectors comes opposites. We call it the non-literal transformation. Literal the transformation y only if it comes from a single x The only remedy is that it is zero at the zero vector space. Zero space as you can see is doing an important task. Now we will move to sample parsed. Before you go to go through these definitions here Getting to know a little time. In these instances we will do well to consolidate these definitions. We will make samples from the two-dimensional space to three-dimensional space, the three-dimensional space to three-dimensional space, We will do five examples, including a four-dimensional space to three dimensional space. Here are some of the two, but three seems As we do so we will be five examples. As you can see three dimensions of space definition, two the size of the target space. The size of the space where the definition of three, three sizes of the target space. Self-small, an equal-dimensional space itself and its own With a large space conversion will try to reinforce these concepts. In addition, we will provide this theorem in these examples.