General Tensor The transformation law (3.14) you can see it iin the other image Definition 7 Definition 7 The generalized vector field V is a tensor of order m = p + q, contravariantof order p(p-contravariant) and covariant of order q(q-covariant), ifits components (T) in (x) and (T)in (¹) obeythe law of transformationдун айта азір охя, джваx x x ²² x¹ x³²tensor general (T) = (TR)$₁828With the obvious range for the free indicesƏxspažja(3.14) Let T = (Tm) be a tensor of the type and order suggested by the Indices. Prove thatS = (T) = (T) is a covariant vector.The transformation law (3.14) for T isI let's do 1= i, m =j and addTx = Tij = ThuTxt = Truklmtuvax ax ax ax axox ox ox ox xmaxi ax ax ax" ôx"ax ax ax axi= Trs= Tirs ak-TEX=T==axtOxkôxi ôx"\ (oxi ox"\ ôxox ox ox ox ox

Given: Tj1 j2 ... jqi1 i2 ... ip=Ts1s2 . . . sqr1r2 . . . rp∂xi1∂xr1∂xi2∂xr2 . . .…

Let T = (Tm) be a tensor of the type and order suggested by the Indices. Prove that S=(T) = (T) is a covariant vector. The transformation law (3.14) for T is let's do Ii, m=j and add Tim Tru T₁ = T = T = ax ax ax ax" əx" tu ax ax ax ax ax dx ax ax ax ax" dx ax ax ax m ax¹ T88% = T Okk (axi ax" tus ex dx = T Əx² =T₁ trs Okk axt Oxk (ax³ ax" êx¹ dx ax ax

Let T = (Tm) be a tensor of the type and order suggested by the Indices. Prove that S=(T) = (T) is a covariant vector. The transformation law (3.14) for T is let's do Ii, m=j and add Tim Tru T₁ = T = T = ax ax ax ax" əx" tu ax ax ax ax ax dx ax ax ax ax" dx ax ax ax m ax¹ T88% = T Okk (axi ax" tus ex dx = T Əx² =T₁ trs Okk axt Oxk (ax³ ax" êx¹ dx ax ax

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section: Chapter Questions

Problem 16RQ

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