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# Trace Of Tensor | Tensor 10 | Trace Of A Tensor

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## Tensor 10 | Trace Of A Tensor

Transcript:

Hi, it’s a bit again, so in this lecture. I’m going to teach you about the test of the cancer. But Mr. Potential is one of the important properties of the tensor that is used in many engineering and do physical Geodynamic application. Especially in many deuteronomy application is the hell intestines, its distance or negative 10 so to find out the pressure or something like that. So you use this test of a tensor, something like that so today? I’m going to teach about the taste of the tensor so to become a test answer or to find out the tensor. Let’s say we have two tenths of C&S and two arbitrary vectors A and B right. Then we have T following T following rules here that must Ts A B should be of it. Okay, number. One, there’s a potential written, something like that beard. This T plus is equal to just of T Plus T so is just of this, and I’m going to prove this later, Okay, number two here, first off arbitrary function E and there isn’t then Alpha T. Yeah, and we have third or something. This of a be equal to a dot B. Okay, so in terms of tensor components or test the components which item test oppress them in like that, Yes, t equal to we can dive down test. T I J E and E. They right circumference of that so SS. So we bring out t I then can I turn here? He is Dot ETA. So from the third is a vector and a the vectors are from that. Yep, got a dot. B then come here. We can also get this Ti ti dot easier, right, So from the following from the feed number. C rolls. So from this, we can write down here. T I and from this rules. We know that if the kronecker delta IJ with Electronica, Delta IJ so from this, we can write down the diagonal part of this, right. I an I or I n j and J. Something I thirsty, right, Yeah, so therefore, we can write down here. So justice of T equal to T 1 1 plus. T 2 plus T P. That means the first of the tensor is nothing but the sum of all the diagonal parts right. So so this, this is the thing this is something like so even that’s why linear law, so we can. I write down here. The essence of T V tensor. It’s called a famous tenses of T. So I’m going to give you an example of that say, For example, we have arbitrary vector here is so we have 1 2 3 4 5 6 a 7 8 9 then the traces of a distance of a would be 1 plus 5 plus 9 So it is peeping right the stiffness of a stick. So if we have another vector set here. D 7 1 T 1 0 of T right over here. We have another t4 okay. What are the tests of the dresses of these nothing? But say seven, plus one plus four equal to seven eight. It’s poor, right, so we can easily get that this is of a plus, that’s it, so so just a soft, something, something like that. So 15 and you have right justice. Zambian taste this is from B and T sub. A is equal to seven and 227 right, so let’s say whether a and a plus B distance of a plus B take there, so a plus B. So what is the a plus B, a plus B equal to chances of it? Let’s be here one a so or the diagonal terms. I’m getting only the diagram term five and six right and to an 11 right and all the terms should be on all. The time should be found or something like that then. What is that chance of that, A plus six plus 11 so what is there? Missy Lebanon, 1717 and eight. What is that? Oh, it didn’t follow that. I think somewhere I made mistake something like that. So I think you have to collect it. Yes, it’s oh oh! I sorry I made a mistake here, so it should be two right here. It should be two here so 7 plus one plus two, so it should be ten so it should be 15 so tests of a plasticizer dresses of a plus dresses of the is here 15 10 is equal to 25 So here it is. Yeah, the 50 right 35 What is that here? It is Unit 5 so test of a plus. B equal to test test of a plus B, So it’s nothing. Yes, yes. This is how many tensor is nothing, but the sum of the diagonal part. Right, let’s diagnose, but yeah, so we have another thing so we can put that easily. It’s very, very easy or something like that. So thank you very much and we can easily prove that. Yeah, that this in the color is the better for you the same way. You can prove this here. This equation, this equation and this equation has is very easy. So you can prove this your socks off. Thank you very much interesting with this lecture, and I’m going to see you on the next clip, thank you!

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