Transcript:
Hi, welcome you again. And in selected. I am going to show you our Fiji about. Angie tents or identity tensor and the cancer in verse, right, so the two gotta pixel here in this letter. Number one identity tensor. I then beauty cancer and inverse stencil in resistance. Alright, so what is adding defense? All I didn’t Answer is nothing but a linear transformation that transforms every vector into itself, right, so I, Nene Tensor is that add anything soul is bad transforms any vector in pin itself. So, for example, here is a vector right and I I is a transformer or is a transform or something like that. Then if I transform a then you can write down, I right, but then if we transform a into itself, that means a then is called. IDG turns out so I. Idi’d need 10 sets in particular, so we can write down here and it until I innocent. You want equal E 1 We know variable is the same right the same way we can write idly tensile. I to equal to e2 and I t equal to 80 Does the components of if you find out components or something like that, then how we can do that? I’d in 10 sir. I I J equal to e. I dot I ETA, right. Yes, so we can that down here. I ii i ii! III door easy. So it’s the Kronecker Delta. So Kronecker Delta is Id returns. Yes, Kronecker. Delta added attention because we have already seen in the previous lecture that if some vectors X the Delta, then the multiplication reasons or the death of the same as the tensor we multiplied by F Kronecker Delta. So what I didn’t intend sold? Our intention is nothing, but the Kronecker Delta shock, Kronecker Delta IJ. So yeah, I say so. What is that it is the same 1 0 0 0 1 0 0 1 0 and watch it so. I think I did need attentive, so you can see. It is obvious that the identity matrix identity matrix is the math pics of I for all the temporal Cartesian coordinate and that so we can let down here, say, say we can also know that if EA equal to 50 a equal to a then sorry, it’s K equal to a then. Definitely t should be I right. I think genetic something like that. For example, I can give you an example here. Say I already gave already example, so if equal to attend source a 1 3 4 5 & 4 5 1 T 2 G 0 then the Ah, then if you multiply a with a identity tensor on Kronecker Delta, then we get 1 3 5 45 1 and 3 20 take the Kronecker Delta R into Matrix, or 13 2 Matrix 0 1 0 0 0 1 0 0 0 1 Then we look at the same result, 1 e 5 45 1 and T 2 0 So we have got the same as a so kronecker delta is and geometric saw right into chance or something like that. Said it right, yes. What is the investments are something like that? So in verse 10 surahs related to the identical, something like this there we have to tensile here. S and T right If two tensors that resulted in salsa where that in such a way that it T with is equal to, I need two metrics here. Let me the Kronecker Delta. Right, Cronica? Deltron something like that. Then we say what we call is equal to T minus 1 That means the inverse tensor in the inverse of is all the university professor, either fine, then the S dying bars of tea and realize these, all right is the invest of T find the components of the inverse of a density to find the inverse of matrix you from the study of mattresses, we know, so is very easy, so inverse of say, presumably inverse of T metrics. Cute empty. Then it must be shown yet. I need to make it to something like that. So it’s very easy, so it’s very easy or something. It tends to intent. So you write down here. T inverse and T is dying to make eternity. I don’t imagine idea if we have transpose or something like that key to the power transpose and I dramatics identity up. There is equal to the teeth to 4-1 It’s transpose so something that is so easy and something you need. You know very well. If you have messy spectrum said yes to the power inverse, minus one equal to S 1 minus S in birds and in inverse so on, Yep, so we know that it’s very easy, so this is because that’s when a tensor is invariable. There is one to one mapping effect or something like that. So it’s very easy easy for you so you can do that. You can use distance or something if you know the physical properties of necklaces, then same as the chance or something like that. Thank you very much for being with us and. I hope you enjoyed this and in the next lecture. I’m going to, I’m going to show you about the orthogonal tensor towards alternative, thank you.