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Write the transformation law of a tensor of order 3 that is 2-contravariant and 1-covariant. Let us take i, j, k, r, s, t p = 2 y q = 1 in Definition 7 and, to avoid unnecessary subscripts, write instead of 1₁, 12, 1, ₁, 2, S1. then (3.14) gives TV = T ‚ax ax ax ax ax axk

Write the transformation law of a tensor of order 3 that is 2-contravariant and 1-covariant. Let us take i, j, k, r, s, t p = 2 y q = 1 in Definition 7 and, to avoid unnecessary subscripts, write instead of 1₁, 12, 1, ₁, 2, S1. then (3.14) gives TV = T ‚ax ax ax ax ax axk

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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General Tensors

definition number 7 is in the other image

Write the transformation law of a tensor of order 3 that is 2-contravariant and 1-covariant. Let us take p = 2 y q = 1 in Definition 7 and, to avoid unnecessary subscripts, write i, j, k, r, s, t instead of 11, 12, 1, 11, 12, S1. then (3.14) gives TV = Tr³ əx¹ x³ ax ax" dx³ dxk
Transcribed Image Text:Write the transformation law of a tensor of order 3 that is 2-contravariant and 1-covariant. Let us take p = 2 y q = 1 in Definition 7 and, to avoid unnecessary subscripts, write i, j, k, r, s, t instead of 11, 12, 1, 11, 12, S1. then (3.14) gives TV = Tr³ əx¹ x³ ax ax" dx³ dxk
Definition 7 The generalized vector field V is a tensor of order m = p + q, contravariant of order p(p-contravariant) and covariant of order q(q-covariant), if its components (T) in (x) and (T)in (¹) obey the law of transformation дун айта азір охя, джва x x x ²² x¹ x³² tensor general (T) = (TR) $₁828 With the obvious range for the free indices Əxsp ažja (3.14)
Transcribed Image Text:Definition 7 The generalized vector field V is a tensor of order m = p + q, contravariant of order p(p-contravariant) and covariant of order q(q-covariant), if its components (T) in (x) and (T)in (¹) obey the law of transformation дун айта азір охя, джва x x x ²² x¹ x³² tensor general (T) = (TR) $₁828 With the obvious range for the free indices Əxsp ažja (3.14)
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